Question

A sinusoidal sound wave moves at 336 m/s through a gas in the positive direction of an x axis. At one instant, gas molecule A is at its maximum displacement in the negative direction of the axis while molecule B is at its equilibrium position. The separation between those molecules is 17.4 cm, and the molecules between A and B have intermediate displacements in the negative direction of the axis. (a) What is the minimum frequency of the sound wave?

In a similar arrangement, for a different sinusoidal sound wave, air molecule C is at its maximum displacement in the positive direction while molecule D is at its maximum displacement in the negative direction. The separation between the molecules is again 17.4 cm, and the molecules between C and D have intermediate displacements. (b) What is the frequency of the sound wave?

Answer 1

Velocity of sound waves, v= 336 m/s

a). Now in this case, molecule A is at maximum Displacement while molecule B is at equilibrium position both on negative direction of axis. At this point distance between molecules are

  

Then Wavelength of this arrangement will be

As this arrangement is depicting only one-fourth of the wave(with one molecule at maximum displacement while other at equilibrium both on same sides of axis), thus displacement between molecules in this will be one-fourth of the wavelength.

then frequency of wave in this will be (ANS)

b). Now in this case, molecule C is at maximum Displacement and molecule D is also at maximum displacement both on opposite direction of axis. At this point distance between molecules are

  

Buth in this Wavelength of this arrangement will be

As this arrangement is depicting only half of the wave(with 2 molecules on there maximum displacement but in opposite direction), thus displacement between molecules in this will be half of the wavelength only.

then frequency of wave in this will be (ANS)