How Fast is the Motorcycle in This Doppler Effect Scenario?

[TheRedDevil18]

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

Homework Equations

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]

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.

 

[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?

 

[Doc Al]

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.

 

[TheRedDevil18]

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

 

[Doc Al]

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

Yes, exactly.

 

[TheRedDevil18]

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

 

[Doc Al]

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

Looks good to me.

 

[TheRedDevil18]

Ok, thanks Doc Al