What's the output of a record needle playing an out-of-speed recordCannibalizing a printer, how to figure out what some of the parts are/doWhat determines the speed of a brushless DC motorDoes the peak torque decrease at rated speed for BLDC motor?What's the relationship between ESC pwm input and output?Controlling the speed of a brushless motor with the HA13535What is the effective speed-control range of a BLDC motor?What's the relationship between DC braking torque and AC turning torque for a given current on a BLDC motorSpeed and position controle of a BLDC motor at the same timeWhat's the best starting point for rotor angle estimation for FOC?How to find the optimal speed of a BLDC motor having hall sensors? Can we change the most efficient speed through the controller?

Why doesn't H₄O²⁺ exist?

Can you really stack all of this on an Opportunity Attack?

Has there ever been an airliner design involving reducing generator load by installing solar panels?

What's that red-plus icon near a text?

If human space travel is limited by the G force vulnerability, is there a way to counter G forces?

What would happen to a modern skyscraper if it rains micro blackholes?

Malformed Address '10.10.21.08/24', must be X.X.X.X/NN or

dbcc cleantable batch size explanation

Can a monk's single staff be considered dual wielded, as per the Dual Wielder feat?

How is the claim "I am in New York only if I am in America" the same as "If I am in New York, then I am in America?

Is it possible to run Internet Explorer on OS X El Capitan?

Perform and show arithmetic with LuaLaTeX

Are astronomers waiting to see something in an image from a gravitational lens that they've already seen in an adjacent image?

Paid for article while in US on F-1 visa?

What's the point of deactivating Num Lock on login screens?

High voltage LED indicator 40-1000 VDC without additional power supply

Revoked SSL certificate

How much RAM could one put in a typical 80386 setup?

Horror movie about a virus at the prom; beginning and end are stylized as a cartoon

Codimension of non-flat locus

A newer friend of my brother's gave him a load of baseball cards that are supposedly extremely valuable. Is this a scam?

Today is the Center

What is the word for reserving something for yourself before others do?

Roll the carpet



What's the output of a record needle playing an out-of-speed record


Cannibalizing a printer, how to figure out what some of the parts are/doWhat determines the speed of a brushless DC motorDoes the peak torque decrease at rated speed for BLDC motor?What's the relationship between ESC pwm input and output?Controlling the speed of a brushless motor with the HA13535What is the effective speed-control range of a BLDC motor?What's the relationship between DC braking torque and AC turning torque for a given current on a BLDC motorSpeed and position controle of a BLDC motor at the same timeWhat's the best starting point for rotor angle estimation for FOC?How to find the optimal speed of a BLDC motor having hall sensors? Can we change the most efficient speed through the controller?






.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;








2












$begingroup$


I'm very interested in vinyl records and analog music, and the belt of my turntable got loose. Upon such situation it piqued my curiosity, what is the output signal at the end of the arm cartridge wires for a known waveshape if the speed is not the correct one.



Say the record was mean to play sin(wt), a pure sine wave, at 33rpm, then, because of a loosen belt or any other reason, it rotates at a different RPM, how to calculate the changes in such sine wave?



I'm not considering the filters that the needle might apply on the signal, whether it is a low pass, band pass, or high pass nor any other impedances that might alter the signal in any circumstance, just a supposedly ideal needle and cartridge.










share|improve this question











$endgroup$


















    2












    $begingroup$


    I'm very interested in vinyl records and analog music, and the belt of my turntable got loose. Upon such situation it piqued my curiosity, what is the output signal at the end of the arm cartridge wires for a known waveshape if the speed is not the correct one.



    Say the record was mean to play sin(wt), a pure sine wave, at 33rpm, then, because of a loosen belt or any other reason, it rotates at a different RPM, how to calculate the changes in such sine wave?



    I'm not considering the filters that the needle might apply on the signal, whether it is a low pass, band pass, or high pass nor any other impedances that might alter the signal in any circumstance, just a supposedly ideal needle and cartridge.










    share|improve this question











    $endgroup$














      2












      2








      2





      $begingroup$


      I'm very interested in vinyl records and analog music, and the belt of my turntable got loose. Upon such situation it piqued my curiosity, what is the output signal at the end of the arm cartridge wires for a known waveshape if the speed is not the correct one.



      Say the record was mean to play sin(wt), a pure sine wave, at 33rpm, then, because of a loosen belt or any other reason, it rotates at a different RPM, how to calculate the changes in such sine wave?



      I'm not considering the filters that the needle might apply on the signal, whether it is a low pass, band pass, or high pass nor any other impedances that might alter the signal in any circumstance, just a supposedly ideal needle and cartridge.










      share|improve this question











      $endgroup$




      I'm very interested in vinyl records and analog music, and the belt of my turntable got loose. Upon such situation it piqued my curiosity, what is the output signal at the end of the arm cartridge wires for a known waveshape if the speed is not the correct one.



      Say the record was mean to play sin(wt), a pure sine wave, at 33rpm, then, because of a loosen belt or any other reason, it rotates at a different RPM, how to calculate the changes in such sine wave?



      I'm not considering the filters that the needle might apply on the signal, whether it is a low pass, band pass, or high pass nor any other impedances that might alter the signal in any circumstance, just a supposedly ideal needle and cartridge.







      brushless-dc-motor






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 2 hours ago









      Dave Tweed

      123k9152266




      123k9152266










      asked 2 hours ago









      Gabriel SantosGabriel Santos

      213




      213




















          4 Answers
          4






          active

          oldest

          votes


















          5












          $begingroup$


          Say the record was mean to play sin(wt), a pure sine wave, at 33rpm, then, because of a loosen belt or any other reason, it rotates at a different RPM, how to calculate the changes in such sine wave?




          The pitch and tempo will change in proportion to the speed change. At 33 RPM it would already be musically flat as the correct speed is 331/3 RPM. A 1 kHz test tone - common on test records - would, at 33 RPM, give off $ frac 3333.33 text kHz $.



          The sinewave would remain a sinewave but stretched in time and, therefore, a lower pitch.






          share|improve this answer











          $endgroup$




















            3












            $begingroup$

            To really simplify, a record has wiggles in the groove that correspond to the recorded sound pressure. (This ignores stereo, and any companding, but it answers your question).



            Events are recorded onto that wiggly grove as they happen -- you can think of the groove as a picture of the sound, with the time domain turned into events happening as the needle follows the groove.



            If you play the record slower, all the events happen more slowly -- the singer sings slower and deeper, the orchestra does too, etc. Speeding it up does the opposite -- a normal recording, sped up, sounds like a hyperactive chipmunk.






            share|improve this answer











            $endgroup$








            • 1




              $begingroup$
              I was surprised when I first learned how records work. It's so analog that it's amazing it works at all.
              $endgroup$
              – Toor
              2 hours ago


















            2












            $begingroup$

            Changing the speed of the platter simply affects how fast the groove is moving under the needle, nothing else.



            A sine wave with the time axis compressed or expanded is still a sine wave. In fact, since the groove is a direct mechanical representation of the original complex waveform, you still get the same waveform simply compressed or expanded in time.






            share|improve this answer









            $endgroup$












            • $begingroup$
              Right, agreed, in the ideal case a a sine wave of same amplitude, but with a diferent frequency, right? The point is for a sin(wt), how the change of rotation speed will affect the frequency?
              $endgroup$
              – Gabriel Santos
              2 hours ago










            • $begingroup$
              It's linear -- double the speed means double the frequency. That's what compressing the time axis means.
              $endgroup$
              – Dave Tweed
              2 hours ago


















            0












            $begingroup$

            Grooves are cut with frequency correction according to RIAA equalization. Playing the record off with wrong speed increases all frequencies by the same factor (corresponding to a shift left/right on the frequency axis of the doubly logarithmic transfer function diagram). Since the frequency correction is not a straight line, this does not just result in a frequency shift but also in an uneven frequency response due to recording and replaying correction no longer being proper inverses.



            In addition, the equalization is done in order to reduce excessive signal amplitudes on stylus and pickup. Counteracting this by wrong speed may lead to either excessive amplitudes (electrical or mechanical) or too low signals overlaid with a relatively higher noise floor.






            share|improve this answer









            $endgroup$













              Your Answer





              StackExchange.ifUsing("editor", function ()
              return StackExchange.using("mathjaxEditing", function ()
              StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
              StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["\$", "\$"]]);
              );
              );
              , "mathjax-editing");

              StackExchange.ifUsing("editor", function ()
              return StackExchange.using("schematics", function ()
              StackExchange.schematics.init();
              );
              , "cicuitlab");

              StackExchange.ready(function()
              var channelOptions =
              tags: "".split(" "),
              id: "135"
              ;
              initTagRenderer("".split(" "), "".split(" "), channelOptions);

              StackExchange.using("externalEditor", function()
              // Have to fire editor after snippets, if snippets enabled
              if (StackExchange.settings.snippets.snippetsEnabled)
              StackExchange.using("snippets", function()
              createEditor();
              );

              else
              createEditor();

              );

              function createEditor()
              StackExchange.prepareEditor(
              heartbeatType: 'answer',
              autoActivateHeartbeat: false,
              convertImagesToLinks: false,
              noModals: true,
              showLowRepImageUploadWarning: true,
              reputationToPostImages: null,
              bindNavPrevention: true,
              postfix: "",
              imageUploader:
              brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
              contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
              allowUrls: true
              ,
              onDemand: true,
              discardSelector: ".discard-answer"
              ,immediatelyShowMarkdownHelp:true
              );



              );













              draft saved

              draft discarded


















              StackExchange.ready(
              function ()
              StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2felectronics.stackexchange.com%2fquestions%2f431010%2fwhats-the-output-of-a-record-needle-playing-an-out-of-speed-record%23new-answer', 'question_page');

              );

              Post as a guest















              Required, but never shown

























              4 Answers
              4






              active

              oldest

              votes








              4 Answers
              4






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes









              5












              $begingroup$


              Say the record was mean to play sin(wt), a pure sine wave, at 33rpm, then, because of a loosen belt or any other reason, it rotates at a different RPM, how to calculate the changes in such sine wave?




              The pitch and tempo will change in proportion to the speed change. At 33 RPM it would already be musically flat as the correct speed is 331/3 RPM. A 1 kHz test tone - common on test records - would, at 33 RPM, give off $ frac 3333.33 text kHz $.



              The sinewave would remain a sinewave but stretched in time and, therefore, a lower pitch.






              share|improve this answer











              $endgroup$

















                5












                $begingroup$


                Say the record was mean to play sin(wt), a pure sine wave, at 33rpm, then, because of a loosen belt or any other reason, it rotates at a different RPM, how to calculate the changes in such sine wave?




                The pitch and tempo will change in proportion to the speed change. At 33 RPM it would already be musically flat as the correct speed is 331/3 RPM. A 1 kHz test tone - common on test records - would, at 33 RPM, give off $ frac 3333.33 text kHz $.



                The sinewave would remain a sinewave but stretched in time and, therefore, a lower pitch.






                share|improve this answer











                $endgroup$















                  5












                  5








                  5





                  $begingroup$


                  Say the record was mean to play sin(wt), a pure sine wave, at 33rpm, then, because of a loosen belt or any other reason, it rotates at a different RPM, how to calculate the changes in such sine wave?




                  The pitch and tempo will change in proportion to the speed change. At 33 RPM it would already be musically flat as the correct speed is 331/3 RPM. A 1 kHz test tone - common on test records - would, at 33 RPM, give off $ frac 3333.33 text kHz $.



                  The sinewave would remain a sinewave but stretched in time and, therefore, a lower pitch.






                  share|improve this answer











                  $endgroup$




                  Say the record was mean to play sin(wt), a pure sine wave, at 33rpm, then, because of a loosen belt or any other reason, it rotates at a different RPM, how to calculate the changes in such sine wave?




                  The pitch and tempo will change in proportion to the speed change. At 33 RPM it would already be musically flat as the correct speed is 331/3 RPM. A 1 kHz test tone - common on test records - would, at 33 RPM, give off $ frac 3333.33 text kHz $.



                  The sinewave would remain a sinewave but stretched in time and, therefore, a lower pitch.







                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited 1 hour ago









                  K H

                  2,360215




                  2,360215










                  answered 2 hours ago









                  TransistorTransistor

                  88.2k785189




                  88.2k785189























                      3












                      $begingroup$

                      To really simplify, a record has wiggles in the groove that correspond to the recorded sound pressure. (This ignores stereo, and any companding, but it answers your question).



                      Events are recorded onto that wiggly grove as they happen -- you can think of the groove as a picture of the sound, with the time domain turned into events happening as the needle follows the groove.



                      If you play the record slower, all the events happen more slowly -- the singer sings slower and deeper, the orchestra does too, etc. Speeding it up does the opposite -- a normal recording, sped up, sounds like a hyperactive chipmunk.






                      share|improve this answer











                      $endgroup$








                      • 1




                        $begingroup$
                        I was surprised when I first learned how records work. It's so analog that it's amazing it works at all.
                        $endgroup$
                        – Toor
                        2 hours ago















                      3












                      $begingroup$

                      To really simplify, a record has wiggles in the groove that correspond to the recorded sound pressure. (This ignores stereo, and any companding, but it answers your question).



                      Events are recorded onto that wiggly grove as they happen -- you can think of the groove as a picture of the sound, with the time domain turned into events happening as the needle follows the groove.



                      If you play the record slower, all the events happen more slowly -- the singer sings slower and deeper, the orchestra does too, etc. Speeding it up does the opposite -- a normal recording, sped up, sounds like a hyperactive chipmunk.






                      share|improve this answer











                      $endgroup$








                      • 1




                        $begingroup$
                        I was surprised when I first learned how records work. It's so analog that it's amazing it works at all.
                        $endgroup$
                        – Toor
                        2 hours ago













                      3












                      3








                      3





                      $begingroup$

                      To really simplify, a record has wiggles in the groove that correspond to the recorded sound pressure. (This ignores stereo, and any companding, but it answers your question).



                      Events are recorded onto that wiggly grove as they happen -- you can think of the groove as a picture of the sound, with the time domain turned into events happening as the needle follows the groove.



                      If you play the record slower, all the events happen more slowly -- the singer sings slower and deeper, the orchestra does too, etc. Speeding it up does the opposite -- a normal recording, sped up, sounds like a hyperactive chipmunk.






                      share|improve this answer











                      $endgroup$



                      To really simplify, a record has wiggles in the groove that correspond to the recorded sound pressure. (This ignores stereo, and any companding, but it answers your question).



                      Events are recorded onto that wiggly grove as they happen -- you can think of the groove as a picture of the sound, with the time domain turned into events happening as the needle follows the groove.



                      If you play the record slower, all the events happen more slowly -- the singer sings slower and deeper, the orchestra does too, etc. Speeding it up does the opposite -- a normal recording, sped up, sounds like a hyperactive chipmunk.







                      share|improve this answer














                      share|improve this answer



                      share|improve this answer








                      edited 6 mins ago

























                      answered 2 hours ago









                      TimWescottTimWescott

                      6,5991416




                      6,5991416







                      • 1




                        $begingroup$
                        I was surprised when I first learned how records work. It's so analog that it's amazing it works at all.
                        $endgroup$
                        – Toor
                        2 hours ago












                      • 1




                        $begingroup$
                        I was surprised when I first learned how records work. It's so analog that it's amazing it works at all.
                        $endgroup$
                        – Toor
                        2 hours ago







                      1




                      1




                      $begingroup$
                      I was surprised when I first learned how records work. It's so analog that it's amazing it works at all.
                      $endgroup$
                      – Toor
                      2 hours ago




                      $begingroup$
                      I was surprised when I first learned how records work. It's so analog that it's amazing it works at all.
                      $endgroup$
                      – Toor
                      2 hours ago











                      2












                      $begingroup$

                      Changing the speed of the platter simply affects how fast the groove is moving under the needle, nothing else.



                      A sine wave with the time axis compressed or expanded is still a sine wave. In fact, since the groove is a direct mechanical representation of the original complex waveform, you still get the same waveform simply compressed or expanded in time.






                      share|improve this answer









                      $endgroup$












                      • $begingroup$
                        Right, agreed, in the ideal case a a sine wave of same amplitude, but with a diferent frequency, right? The point is for a sin(wt), how the change of rotation speed will affect the frequency?
                        $endgroup$
                        – Gabriel Santos
                        2 hours ago










                      • $begingroup$
                        It's linear -- double the speed means double the frequency. That's what compressing the time axis means.
                        $endgroup$
                        – Dave Tweed
                        2 hours ago















                      2












                      $begingroup$

                      Changing the speed of the platter simply affects how fast the groove is moving under the needle, nothing else.



                      A sine wave with the time axis compressed or expanded is still a sine wave. In fact, since the groove is a direct mechanical representation of the original complex waveform, you still get the same waveform simply compressed or expanded in time.






                      share|improve this answer









                      $endgroup$












                      • $begingroup$
                        Right, agreed, in the ideal case a a sine wave of same amplitude, but with a diferent frequency, right? The point is for a sin(wt), how the change of rotation speed will affect the frequency?
                        $endgroup$
                        – Gabriel Santos
                        2 hours ago










                      • $begingroup$
                        It's linear -- double the speed means double the frequency. That's what compressing the time axis means.
                        $endgroup$
                        – Dave Tweed
                        2 hours ago













                      2












                      2








                      2





                      $begingroup$

                      Changing the speed of the platter simply affects how fast the groove is moving under the needle, nothing else.



                      A sine wave with the time axis compressed or expanded is still a sine wave. In fact, since the groove is a direct mechanical representation of the original complex waveform, you still get the same waveform simply compressed or expanded in time.






                      share|improve this answer









                      $endgroup$



                      Changing the speed of the platter simply affects how fast the groove is moving under the needle, nothing else.



                      A sine wave with the time axis compressed or expanded is still a sine wave. In fact, since the groove is a direct mechanical representation of the original complex waveform, you still get the same waveform simply compressed or expanded in time.







                      share|improve this answer












                      share|improve this answer



                      share|improve this answer










                      answered 2 hours ago









                      Dave TweedDave Tweed

                      123k9152266




                      123k9152266











                      • $begingroup$
                        Right, agreed, in the ideal case a a sine wave of same amplitude, but with a diferent frequency, right? The point is for a sin(wt), how the change of rotation speed will affect the frequency?
                        $endgroup$
                        – Gabriel Santos
                        2 hours ago










                      • $begingroup$
                        It's linear -- double the speed means double the frequency. That's what compressing the time axis means.
                        $endgroup$
                        – Dave Tweed
                        2 hours ago
















                      • $begingroup$
                        Right, agreed, in the ideal case a a sine wave of same amplitude, but with a diferent frequency, right? The point is for a sin(wt), how the change of rotation speed will affect the frequency?
                        $endgroup$
                        – Gabriel Santos
                        2 hours ago










                      • $begingroup$
                        It's linear -- double the speed means double the frequency. That's what compressing the time axis means.
                        $endgroup$
                        – Dave Tweed
                        2 hours ago















                      $begingroup$
                      Right, agreed, in the ideal case a a sine wave of same amplitude, but with a diferent frequency, right? The point is for a sin(wt), how the change of rotation speed will affect the frequency?
                      $endgroup$
                      – Gabriel Santos
                      2 hours ago




                      $begingroup$
                      Right, agreed, in the ideal case a a sine wave of same amplitude, but with a diferent frequency, right? The point is for a sin(wt), how the change of rotation speed will affect the frequency?
                      $endgroup$
                      – Gabriel Santos
                      2 hours ago












                      $begingroup$
                      It's linear -- double the speed means double the frequency. That's what compressing the time axis means.
                      $endgroup$
                      – Dave Tweed
                      2 hours ago




                      $begingroup$
                      It's linear -- double the speed means double the frequency. That's what compressing the time axis means.
                      $endgroup$
                      – Dave Tweed
                      2 hours ago











                      0












                      $begingroup$

                      Grooves are cut with frequency correction according to RIAA equalization. Playing the record off with wrong speed increases all frequencies by the same factor (corresponding to a shift left/right on the frequency axis of the doubly logarithmic transfer function diagram). Since the frequency correction is not a straight line, this does not just result in a frequency shift but also in an uneven frequency response due to recording and replaying correction no longer being proper inverses.



                      In addition, the equalization is done in order to reduce excessive signal amplitudes on stylus and pickup. Counteracting this by wrong speed may lead to either excessive amplitudes (electrical or mechanical) or too low signals overlaid with a relatively higher noise floor.






                      share|improve this answer









                      $endgroup$

















                        0












                        $begingroup$

                        Grooves are cut with frequency correction according to RIAA equalization. Playing the record off with wrong speed increases all frequencies by the same factor (corresponding to a shift left/right on the frequency axis of the doubly logarithmic transfer function diagram). Since the frequency correction is not a straight line, this does not just result in a frequency shift but also in an uneven frequency response due to recording and replaying correction no longer being proper inverses.



                        In addition, the equalization is done in order to reduce excessive signal amplitudes on stylus and pickup. Counteracting this by wrong speed may lead to either excessive amplitudes (electrical or mechanical) or too low signals overlaid with a relatively higher noise floor.






                        share|improve this answer









                        $endgroup$















                          0












                          0








                          0





                          $begingroup$

                          Grooves are cut with frequency correction according to RIAA equalization. Playing the record off with wrong speed increases all frequencies by the same factor (corresponding to a shift left/right on the frequency axis of the doubly logarithmic transfer function diagram). Since the frequency correction is not a straight line, this does not just result in a frequency shift but also in an uneven frequency response due to recording and replaying correction no longer being proper inverses.



                          In addition, the equalization is done in order to reduce excessive signal amplitudes on stylus and pickup. Counteracting this by wrong speed may lead to either excessive amplitudes (electrical or mechanical) or too low signals overlaid with a relatively higher noise floor.






                          share|improve this answer









                          $endgroup$



                          Grooves are cut with frequency correction according to RIAA equalization. Playing the record off with wrong speed increases all frequencies by the same factor (corresponding to a shift left/right on the frequency axis of the doubly logarithmic transfer function diagram). Since the frequency correction is not a straight line, this does not just result in a frequency shift but also in an uneven frequency response due to recording and replaying correction no longer being proper inverses.



                          In addition, the equalization is done in order to reduce excessive signal amplitudes on stylus and pickup. Counteracting this by wrong speed may lead to either excessive amplitudes (electrical or mechanical) or too low signals overlaid with a relatively higher noise floor.







                          share|improve this answer












                          share|improve this answer



                          share|improve this answer










                          answered 44 mins ago







                          user217611


































                              draft saved

                              draft discarded
















































                              Thanks for contributing an answer to Electrical Engineering Stack Exchange!


                              • Please be sure to answer the question. Provide details and share your research!

                              But avoid


                              • Asking for help, clarification, or responding to other answers.

                              • Making statements based on opinion; back them up with references or personal experience.

                              Use MathJax to format equations. MathJax reference.


                              To learn more, see our tips on writing great answers.




                              draft saved


                              draft discarded














                              StackExchange.ready(
                              function ()
                              StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2felectronics.stackexchange.com%2fquestions%2f431010%2fwhats-the-output-of-a-record-needle-playing-an-out-of-speed-record%23new-answer', 'question_page');

                              );

                              Post as a guest















                              Required, but never shown





















































                              Required, but never shown














                              Required, but never shown












                              Required, but never shown







                              Required, but never shown

































                              Required, but never shown














                              Required, but never shown












                              Required, but never shown







                              Required, but never shown







                              Popular posts from this blog

                              How should I use the fbox command correctly to avoid producing a Bad Box message?How to put a long piece of text in a box?How to specify height and width of fboxIs there an arrayrulecolor-like command to change the rule color of fbox?What is the command to highlight bad boxes in pdf?Why does fbox sometimes place the box *over* the graphic image?how to put the text in the boxHow to create command for a box where text inside the box can automatically adjust?how can I make an fbox like command with certain color, shape and width of border?how to use fbox in align modeFbox increase the spacing between the box and it content (inner margin)how to change the box height of an equationWhat is the use of the hbox in a newcommand command?

                              Doxepinum Nexus interni Notae | Tabula navigationis3158DB01142WHOa682390"Structural Analysis of the Histamine H1 Receptor""Transdermal and Topical Drug Administration in the Treatment of Pain""Antidepressants as antipruritic agents: A review"

                              Haugesund Nexus externi | Tabula navigationisHaugesund pagina interretialisAmplifica