Sinusoidal Pressure Wave: Questions & Answers

In summary, a sinusoidal pressure wave with a displacement amplitude of 1cm in a gas with a density of 2 kg m-3 and a velocity of 10 m s-1 has a bulk modulus of 2000 Pa and a wavelength of 20 m if its temporal frequency is 1 kHz. To become sub-supersonic, the frequency of the wave must be increased by a factor of 10.
  • #1
Plaetean
36
0

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=[itex]\sqrt{B/ρ}[/itex]


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.
 
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  • #2
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.
 
  • #3
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.
 
  • #4
BiGyElLoWhAt said:
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?
 
  • #5
Plaetean said:
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?
 
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  • #6
haruspex said:
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.
 
  • #7
haruspex said:
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!

z09JPog.png


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

What is a sinusoidal pressure wave?

A sinusoidal pressure wave is a type of wave that occurs when a pressure disturbance travels through a medium, such as air or water, in a sinusoidal pattern. This means that the pressure disturbance varies in a smooth, repetitive motion over time, resembling a sine wave.

How are sinusoidal pressure waves created?

Sinusoidal pressure waves can be created by a variety of sources, including sound waves, seismic waves, and ocean waves. They can also be generated by machines and equipment, such as pumps and compressors, that produce changes in pressure within a system.

What are the characteristics of a sinusoidal pressure wave?

The main characteristics of a sinusoidal pressure wave include its amplitude, wavelength, frequency, and speed. The amplitude is the maximum height of the wave, the wavelength is the distance between two consecutive peaks or troughs, the frequency is the number of cycles per second, and the speed is the rate at which the wave travels through the medium.

How are sinusoidal pressure waves measured and analyzed?

Sinusoidal pressure waves can be measured and analyzed using various tools and techniques, such as pressure sensors, oscilloscopes, and mathematical formulas. The measurements and analysis can provide valuable information about the properties and behavior of the wave, such as its intensity, direction, and propagation speed.

What are the applications of sinusoidal pressure waves?

Sinusoidal pressure waves have numerous applications in various fields, including acoustics, geophysics, engineering, and medicine. They are used to study and understand the behavior of fluids and gases, to detect and measure seismic activity, and to transmit and receive sound signals. They are also utilized in medical imaging techniques, such as ultrasound, to create images of internal structures and organs.

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