How Fast is the Motorcycle in This Doppler Effect Scenario?

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Homework Help Overview

The discussion revolves around a Doppler effect scenario involving a motorcycle that emits a sound frequency of 6000Hz. The problem presents a frequency shift of 30Hz as the motorcycle approaches and then recedes from the observer, with the speed of sound given as 340m/s.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the frequency shifts and the speed of the motorcycle, considering the equations related to the Doppler effect. There are attempts to set up equations based on the frequency shifts and to solve for the speed of the motorcycle.

Discussion Status

Several participants have proposed methods to set up equations to find the speed of the motorcycle, with some confirming the validity of these approaches. There is an ongoing exploration of how to correctly interpret the frequency shifts and apply the Doppler effect equations.

Contextual Notes

Participants question the assumptions about the motorcycle's speed being constant during the approach and recession phases, as well as the interpretation of the frequency shift of 30Hz.

TheRedDevil18
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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?
 
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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.
 
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?
 
TheRedDevil18 said:
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?
 
TheRedDevil18 said:
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?
 
TheRedDevil18 said:
Speed of the motorcycle worked out to be 0.85m/s, correct?
Looks good to me.
 
Ok, thanks Doc Al
 

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