Why is the speed of sound from a jet moving at 100m/s through air still 340m/s?

[Gear2d]

Homework Statement

Speed of sound in air is 340m/s. Sound from a jet, moving a 100m/s through the air, will have a speed of:

Homework Equations

Doppler effect, and v = Sqrt(bulk/density)

The Attempt at a Solution

The answer for this is 340m/s. I was wondering why. Because all the book states is that wave velocity is INDEPENDENT of medium (I thought velocity of a wave was medium dependent).

 

[Doc Al]

The answer for this is 340m/s. I was wondering why.

The velocity of sound is 340 m/s with respect to the medium (air). The point of the exercise is that the speed of the source (the jet) is irrelevant.

Because all the book states is that wave velocity is INDEPENDENT of medium (I thought velocity of a wave was medium dependent).

That's a pretty wild statement. You're right, the speed of sound most definitely depends on the medium. (What book is that, by the way?) What was the context of that statement?

 

[baba89]

I can provide a more detailed explanation for why the speed of sound from a jet moving at 100m/s through the air is still 340m/s. The speed of sound is determined by the properties of the medium it is traveling through, such as air density and elasticity. In this case, the medium is air, with a density of approximately 1.2 kg/m^3. The speed of sound in air is given by the equation v = √(γRT), where γ is the adiabatic index (which is 1.4 for air), R is the gas constant, and T is the temperature in Kelvin. For air at room temperature, this equation yields a speed of sound of approximately 340m/s.

Now, the Doppler effect comes into play when the source of the sound (in this case, the jet) is moving relative to the observer. The Doppler effect causes a shift in the frequency of the sound waves, but it does not affect the speed of the waves themselves. This means that even though the jet is moving at 100m/s, the speed of the sound waves it produces is still 340m/s. This is because the speed of the sound waves is determined by the medium, not the motion of the source.

In summary, the speed of sound from a jet moving at 100m/s through air is still 340m/s because the speed of sound is determined by the properties of the medium, and the Doppler effect only affects the frequency of the sound waves, not their speed.