# Doppler Effect Problem

1. Apr 13, 2013

### TheRedDevil18

1. The problem statement, all variables and given/known data

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

2. Relevant equations

fl = fs(v/v-vs)

3. 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?

2. Apr 13, 2013

### Staff: 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.

3. Apr 13, 2013

### TheRedDevil18

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?

4. Apr 13, 2013

### Staff: Mentor

Sounds good to me.

5. Apr 13, 2013

### TheRedDevil18

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

6. Apr 13, 2013

### Staff: Mentor

Yes, exactly.

7. Apr 13, 2013

### TheRedDevil18

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

8. Apr 13, 2013

### Staff: Mentor

Looks good to me.

9. Apr 13, 2013

### TheRedDevil18

Ok, thanks Doc Al