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I was reading waves from H.C. Verma in which it was written when two sound sources vibrate in unison then at mid point between the sources a pressure antinode is produced but a displacement node .

And for this detector at mid point detect maximum intensity so it more appropriate to consider sound as a pressure wave then as a displacement wave and on rational thinking it feels to be correct.

but when i tried to prove this statement mathematically i found that at mid point pressure as well as displacement antinode are formed

could you plz provide me right proof of this statement

I'm trying to post the statement from hc verma as well as my mathematically derivation, but unfortunately stackexchange shows that something went wrong, plz try again later.

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  • $\begingroup$ When considering acoustic waves in a fluid the pressure and local particle velocity, or displacement field, are related. The pressure field is proportional to the derivative of the particle displacement amplitude, or vice verse. For a time harmonic source these will be 90deg out of phase, e.g. one will have an anti node where the other has a node. $\endgroup$
    – user196418
    Apr 6, 2020 at 20:17

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it depends of the wavelength or frequency of your source, you can have a pressure knot or a displacement knot, the max of pressure ist the min of displacement . And no it is not always in the middle.

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  • $\begingroup$ you interpreted my question wrongly $\endgroup$ Apr 6, 2020 at 0:32
  • $\begingroup$ so how can you prove :but when i tried to prove this statement mathematically i found that at mid point pressure as well as displacement antinode are formed? $\endgroup$
    – trula
    Apr 6, 2020 at 19:34
  • $\begingroup$ i took two sinusoidal sound wave equation travelling in opposite directions , all other parameters were same , then I superposed the waves at the centre of the sources. I'm trying to post my derivation but I'm unable to $\endgroup$ Apr 6, 2020 at 20:06
  • $\begingroup$ what is the distance to the middle measured in wavelength? $\endgroup$
    – trula
    Apr 7, 2020 at 14:36

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