# Sound waves and speed of it in different reference frames

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)

Doc Al
Mentor
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.

physics user1
physics user1
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?

Doc Al
Mentor
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.

Ain't the cop and the person in relative motion?
Definitely.

physics user1
Basically, it will travel slower relative to the car and the speed of sound relative to the ground

physics user1