# Doppler Effect Problem

## Homework Statement

A hooter on a motorcycle sounds a note of 6000Hz when the motorcycle is stationary. You detect a shift in frequency of 30Hz when the motorcycle approaches you and then recedes from you. Calculate the speed of the motorcycle.
Speed of sound = 340m/s

fl = fs(v/v-vs)

## The Attempt at a Solution

When motorcycle approaches:

fl = (v/v-vs)
6030 = (340/340-vs)
vs = 16.58m/s

When motorcycle recedes:

fl = (v/v+vs)
5070 = (340/340+vs)
vs = 54.48m/s

Is this correct?

Doc Al
Mentor
I believe that the problem intends that the motorcycle moves towards you, then passes you by, always moving at the same speed. 30 Hz is the difference between those two frequencies.

So fl-fl prime = 30Hz ? , so if I set up two equations, fl = fs(v/v-vs) and fl prime = fs(v/v+vs) and then subtract them and equate to 30 and solve for vs, will that be right?

Doc Al
Mentor
So fl-fl prime = 30Hz ? , so if I set up two equations, fl = fs(v/v-vs) and fl prime = fs(v/v+vs) and then subtract them and equate to 30 and solve for vs, will that be right?
Sounds good to me.

6000(340/340-vs) - 6000(340/340+vs) = 30
Is that how I would set up the equation?

Doc Al
Mentor
6000(340/340-vs) - 6000(340/340+vs) = 30
Is that how I would set up the equation?
Yes, exactly.

Speed of the motorcycle worked out to be 0.85m/s, correct?

Doc Al
Mentor
Speed of the motorcycle worked out to be 0.85m/s, correct?
Looks good to me.

Ok, thanks Doc Al