Negative pressure sound wave?

Question

A 80Hz sound pressure wave can be heard by most humans

By the doppler effect, if a loudspeaker is installed in the back of a car, pointed to the rear, issuing 80Hz sinusoidal waveform and if the car is travelling away from you at 100m/s (360km/h) you will hear that pressure wave at 56.470Hz.

Formula is:

Frequency * (SpeedOfSound - CarSpeed) / SpeedOfSound

80 * (340-100) / 340

Now, if the car is traveling at 400m/s (1,440km/h), the pressure wave will have a frequency of;

80 * (340 - 400) / 340 = -14.11Hz (negative)

Well, it is very strange to think about a negative frequency, but the pressure wave will indeed be negative (above sound speed barrier).

How can you hear a negative pressure wave? even if your ear canal is directly pointing to speaker traveling away of you? you can not, right?

You can't ear it since the source is traveling away faster than the waves can move toward you;

But the technical explanation would be;

1) Because the pressure waves are negative.

2) Because the frequency is negative.

Choose one.

Negative pressure waves can be reproduced in your desk, just use a vacuum chamber and a controlled valve allowing air to leak into the chamber at 80Hz sinusoidal pressure. It is a reverse of a loudspeaker.

In a loudspeaker you have positive and negative pressure waves. In the vacuum chamber experiment you will have zero pressure or negative pressure, never positive pressure exiting the valve.

But negative frequency is impossible to generate.

What is the best explanation?

Answer 1

The best explanation is that the velocity of the air at the air/speaker interface is effectively zero relative to the speaker, and as you move away, the air velocity relative to the speaker increases until it reaches 400m/s.  

You can imagine this as a vortex circling around the outside of the speaker like an eddy behind a rock in a stream.

What would happen is that the sound wave would leave the loudspeaker pushing the local air, which would then push the air next to it (this air is moving), and so on and so on until the sound wave reach stable air, i.e., air that did not have a significant differential in velocity.  Here is an example of an earlier question I answered regards sound wave where there is a velocity differential:  http://answers.yahoo.com/question/index;...

The moving air would also have the effect of focusing the sound waves directly behind the speaker.  The frequency would be lower based on the doppler, but it wouldn't go negative.  The sound wave disbursement would also be limited to the supersonic shock wave caused by the truck, the sound wave would never get past that.

The key is figuring out what the velocity differential is in the air behind the speaker.  You are going to need to do a lot of experimentation to figure that one out.  Here is something to help you out: http://www.ifh.uni-karlsruhe.de/people/t...

Vacuum dispersal question is very interesting.  The velocity of the gas is equal or exceeds the speed of sound.  Two thoughts, first, things act funny in a vacuum.  The mean free path of the gas molecules would probably exceed the wavelength of the sound -- I'm not sure if sound could be effectively trasmitted in those conditions. The second thought is that in measuring pressure, you have to look at position.  Put a measuring plate in front of the valve and you will measure positive pressure everywhere.  But behind the plate you would have a vacuum and measure nothing.

Answer 2

your formula’s wrong! Doppler says:

f=f0/(1 +u/v) – no negative f;

neither negative pressure!

Answer 3

The correct answer you have, the generator is traveling away from the listener at faster than the speed of sound.

Now you have to choose between two incorrect answers, I'd just flip a coin and include in large letters that neither one is the correct answer.

Negative pressure is still perceived by the ear as pressure. Don't forget every sinusoidal pressure wave goes both positive and negative.

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