Sound waves and speed of it in different reference frames

So, in summary, the speed of sound emitted by a moving cop car will be measured as C - Vc by a person at rest with respect to the air, due to the Galilean equations and the Doppler effect. The cop car and person are in relative motion, which affects the speed of sound as measured by the cop.
  • #1
physics user1
Think at a cop car with a siren that moves with a velocity Vc, it emits a sound with a velocity C

Now think about a person that doesn't move, in front of the cop car, shouldn't he register that the speed of the sound emited is Vs= Vc+ C?

According to the galileian equations (true for v <<c light)

x= x' + Vc t (distance done by the sound wave according to the guy in front of the cop car)
x'= Ct (distance done by the sound wave according to the cop car frame of reference)

x= (C+ Vc) t

d/dt x = d/dt [ (C+Vc) t]

Vs= C + Vc

Is that correct? Does the speed of the wave change with the frame of reference?

Is because of that that the frequency changes? (Doppler effect)
 
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  • #2
Cozma Alex said:
Now think about a person that doesn't move, in front of the cop car, shouldn't he register that the speed of the sound emited is Vs= Vc+ C?
No.

Realize that the speed of sound is C with respect to its medium, the air. So a person at rest with respect to the air will measure the speed of the sound as C.
 
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  • #3
Doc Al said:
No.

Realize that the speed of sound is C with respect to its medium, the air. So a person at rest with respect to the air will measure the speed of the sound as C.

and... the cop? Why is he registering the same speed?

Ain't the cop and the person in relative motion?
 
  • #4
Cozma Alex said:
and... the cop? Why is he registering the same speed?
He's not. Here's the basic formula:
Speed of sound with respect to cop = Speed of sound w.r.t. air + speed of air w.r.t cop = C - Vc.

Cozma Alex said:
Ain't the cop and the person in relative motion?
Definitely.
 
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  • #5
Basically, it will travel slower relative to the car and the speed of sound relative to the ground
 
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1. What is a sound wave and how does it travel?

A sound wave is a type of mechanical wave that is created by vibrations in a medium, such as air or water. These vibrations cause the particles in the medium to move back and forth, creating a series of compressions and rarefactions that travel through the medium.

2. How does the speed of sound vary in different reference frames?

The speed of sound is dependent on the properties of the medium through which it is traveling. In general, the speed of sound is faster in more rigid and dense materials, such as solids, and slower in less dense materials, such as gases. Additionally, the speed of sound can be affected by factors such as temperature and humidity.

3. How is the speed of sound affected by temperature and humidity?

As the temperature of a medium increases, the speed of sound also increases. This is because the molecules in the medium have more energy, allowing them to vibrate at a faster rate. Humidity, or the amount of water vapor in the air, can also affect the speed of sound. In general, higher humidity levels can slow down the speed of sound.

4. How does the speed of sound in air compare to other materials?

The speed of sound in air at room temperature is approximately 343 meters per second. This is much slower than the speed of sound in other materials, such as water (1500 m/s) and steel (6000 m/s). However, sound can travel much faster in certain gases, such as helium, which has a speed of sound of 965 m/s.

5. How is the speed of sound measured and calculated?

The speed of sound can be measured using various techniques, such as an oscilloscope or a sound level meter. It can also be calculated using the formula v = fλ, where v is the speed of sound, f is the frequency of the sound wave, and λ is the wavelength. This formula takes into account the relationship between the speed, frequency, and wavelength of a wave.

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