Doppler Effect: Speed of Sound and Wind Question

[Perrin]

Hi, I've got a problem that I can't seem to find an explanation to, about the Doppler Effect

An ambulance is going down the road at a speed U meters/second, in the same direction as the wind, which has a speed of W meters/second. The speed of sound in air is c meters/second

Now, I have to choose one of three options:

1) always c>U+W
2) always c<U+W
3) neither (1) nor (2)

At first I thought that the correct answer was (3), because I couldn't think of a reason why there should be a restriction to the speed of sound in air.
The correct answer is (1) though, and I can't understand why.
Can someone please enlighten me?
Thanks for the help.

 

[bucher]

I think the reason why it's 1 is because you're assuming that the ambulance isn't breaking the sound barrier. The speed of sound is a constant (it can change due to temperature but we'll assume it's a constant for this problem).

Also, considering the two other choices, either "c" is less than "U + W" which is obviously false or "c" is equal to "U + W" (assuming it's what is implied) which is also false.

 

[Perrin]

Is there something conceptually wrong with option 2?
Let me see if I understand correctly. If the wind has a certain velocity, the resulting velocity of the sound wave is the constant velocity, 343m/s, plus the velocity of the wind. So, is there a reason why option 2 cannot occur?

 

[bucher]

I don't think that there is anything wrong with the concept of option 2. But for this problem, I think that they want you to assume reasonable speeds for both the ambulance and the wind.

For example, option 2 would be correct if the ambulance was going above Mach 1. But how reasonable is that?

I think it may have something to do with the book the problem came from. Maybe it typically assumes the ordinary.

 

[Perrin]

Thanks for the explanation!