Sinusoidal Pressure Wave: Questions & Answers

[Plaetean]

Homework Statement

Consider a sinusoidal pressure wave in a gas with a fixed displacement amplitude of 1cm. The gas has a density of 2 kg m-3 and the wave travels at a velocity of 10 m s-1.
a) What is the bulk modulus of the gas? [3]
b) What is the wavelength of the wave if its temporal frequency is 1 kHz? [2]
c) By what factor must the frequency of the wave be increased for it to become sub-supersonic?

Homework Equations

v=fl=\sqrt{B/ρ}

The Attempt at a Solution

a) and b) I can answer fine, but I have no idea what c) is even asking. I have a solution sheet, and the solution is given here, but I can't follow it at all I'm afraid.

 

[BiGyElLoWhAt]

I'm not entirely sure, but I think what it's saying is currently, the frequency is supersonic, or f>the highest frequency sound waves.
By what factor must the frequency be increased so that f ≤ the highest frequency sound wave.
https://www.google.com/#q=soundwave+frequency+range

But my thing is: Perhaps they mean period? If it's supersonic, and you increase the frequency, it's not going to become sub-supersonic... Unless they want an answer less than 1, then the question is just poorly worded.

 

[BiGyElLoWhAt]

Just looked at the answer, and yes, the question is either a) poorly worded, or b) copied wrong.

So calculate the frequency of your wave, and take the ratio to find the factor you need to multiply it by to arrive at a frequency lower than supersonic.

 

[Plaetean]

Just looked at the answer, and yes, the question is either a) poorly worded, or b) copied wrong.

So calculate the frequency of your wave, and take the ratio to find the factor you need to multiply it by to arrive at a frequency lower than supersonic.

Sorry if I'm missing something extremely basic, but how do you know what the 'supersonic' frequency is?

 

[haruspex]

Sorry if I'm missing something extremely basic, but how do you know what the 'supersonic' frequency is?

I'm only guessing here, but...
Consider the motion of the gas molecules. With a sinusoidal motion of amplitude 1cm and a given frequency, how fast do the molecules have to move at peak speed during oscillation? How does that compare with the speed of a sound wave in the medium?

 

[Plaetean]

I'm only guessing here, but...
Consider the motion of the gas molecules. With a sinusoidal motion of amplitude 1cm and a given frequency, how fast do the molecules have to move at peak speed during oscillation? How does that compare with the speed of a sound wave in the medium?

Ahhh that must be it, thanks, I would never have thought of that on my own, question doesn't make it clear at all.

 

[Plaetean]

I'm only guessing here, but...
Consider the motion of the gas molecules. With a sinusoidal motion of amplitude 1cm and a given frequency, how fast do the molecules have to move at peak speed during oscillation? How does that compare with the speed of a sound wave in the medium?

Sorry to bump this, but I've tried following through the problem along that line of thought and still can't reproduce the answer in the solutions sheet. If anyone understands how this problem is solved please could you enlighten me!

edit: **** I just figured it out, I had missed a factor of 2pi, sorry guys