Question

You are listening to a trumpet that is playing a note at 210 Hz. You decide that this doesn’t sound quite right, and you’d rather listen to it at 228 Hz.

Part a.) Which direction can you move so that the trumpet will sound like it’s playing 228 Hz?

Part b.) How fast should you move in that direction?

Part c.) What if you could get the trumpet to move instead (while you stay still)? What direction should the trumpet move so that it will sound to you like it’s playing 228 Hz?

need help with all parts please show all work and formulas used thanks :)

Answer 1

a)
The change in frequency according to the doppler effect is,
f = fo [(C Vr) / (C Vs)]
Where C is the velocity of sound, Vr is the velocity of the receiver and Vs is the velocity of the source.
C Vr = C + Vr if the receiver is moving toward the source of sound
C Vr = C - Vr if the receiver is moving away from the source of sound
C Vs = C - Vs if the source is moving toward the receiver
C Vs = C + Vs if the source is moving away from the receiver.

So according to the above equation, frequency will increase if you (receiver) move toward the direction of the trumpet (source)

b)
From the previous equation,
f = fo[(C + Vr) / (C + 0)]
228 = 210 [(343 + Vr) / 343]
228/210 = 1 + Vr/343
Vr/343 = 0.0857
Vr = 343 x 0.0857
= 29.4 m/s

c)
Here the velocity of you (receiver) is zero, but the trumpet(source) move toward you with a velocity Vs,
f = fo [C/(C - Vs)]
fo/f = (C - Vs) / C
210/228 = 1 - Vs/343
Vs/343 = 0.0789
Vs = 343 x 0.0789
= 27.08 m/s