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

In summary, the speed of sound in air is 340m/s and is independent of the speed of the source (in this case, a jet moving at 100m/s). The speed of sound is dependent on the medium it travels through, and the equation for calculating it involves the Doppler effect and the bulk and density of the medium. The statement that wave velocity is independent of medium is incorrect and may have been taken out of context.
  • #1
Gear2d
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0

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).
 
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  • #2
Gear2d said:
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?
 
  • #3


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.
 

1. What is the Doppler effect?

The Doppler effect is the change in frequency or wavelength of a wave relative to an observer who is moving relative to the source of the wave. This effect is commonly observed with sound waves, where a moving source will cause a change in the perceived pitch of the sound.

2. How does the Doppler effect affect the velocity of a wave?

The Doppler effect does not directly affect the velocity of a wave. It only changes the frequency or wavelength of the wave as perceived by an observer. The actual velocity of the wave remains constant.

3. What factors influence the Doppler effect?

The main factors that influence the Doppler effect are the relative velocities of the wave source and the observer, as well as the speed of the wave itself. Additionally, the medium through which the wave is traveling can also affect the perceived frequency or wavelength.

4. How is the Doppler effect used in real life applications?

The Doppler effect has various practical applications, such as in radar and sonar systems, where it is used to measure the velocity of moving objects. It is also used in medical imaging techniques, such as ultrasound, to detect and monitor blood flow. In astronomy, the Doppler effect is used to determine the velocity of celestial objects.

5. Can the Doppler effect be observed with all types of waves?

Yes, the Doppler effect can be observed with any type of wave, including sound waves, light waves, and water waves. However, the perceived change in frequency or wavelength may vary depending on the type of wave and the relative velocities of the source and observer.

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