Doppler Effect Problem

  • #1

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?
 

Answers and Replies

  • #2
Doc Al
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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
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
Doc Al
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45,140
1,439
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.
 
  • #5
6000(340/340-vs) - 6000(340/340+vs) = 30
Is that how I would set up the equation?
 
  • #6
Doc Al
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6000(340/340-vs) - 6000(340/340+vs) = 30
Is that how I would set up the equation?
Yes, exactly.
 
  • #7
Speed of the motorcycle worked out to be 0.85m/s, correct?
 
  • #8
Doc Al
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45,140
1,439
Speed of the motorcycle worked out to be 0.85m/s, correct?
Looks good to me.
 
  • #9
Ok, thanks Doc Al
 

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