Doppler effect car horn question

In summary: So, in summary, a policeman with a good understanding of the Doppler effect was able to determine that a car was speeding by hearing a change in the pitch of its horn. Using the formula for the Doppler effect, he was able to calculate the speed of the car, which was over the speed limit. This justified him in pulling the motorist over and issuing a speeding ticket.
  • #1
yjk91
75
0

Homework Statement



A policeman with a very good ear and a good understanding of the Doppler effect stands on the shoulder of a freeway assisting a crew in a 40-mph work zone. He notices a car approaching that is honking its horn. As the car gets closer, the policeman hears the sound of the horn as a distinct B4 tone (494 Hz). The instant the car passes by, he hears the sound as a distinct A4 tone (440 Hz). He immediately jumps on his motorcycle, stops the car, and gives the motorist a speeding ticket. Explain his reasoning.


The Attempt at a Solution


f0 = f (V(sound) / (V(sound) - V(source)))
since the car is moving toward the policemen it is negative
so
494Hz = 440Hz * (343 v/s / (343 - V))
and V is 37.166 m/s...
which is obviously not..
i'm not sure where i went wrong probably doppler effect..

thank you
 
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  • #2
Well, I haven't really gone through any of the calculations in your problem... but... just off an initial glance I saw you came up with:

V = 37.166 m/s

Which is a decent answer. And you need to prove that this motorist was speeding past the limit of 40 mph... perhaps a conversion? Doing so would put the motorist's speed at ~80mph which is certainly justifiable for the policeman to pull the motorist over. Or maybe I'm misinterpreting what you're looking for here.
 
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  • #3
i converted to mph from m/s
and i got 83 mph which still is the wrong answer
i think it's the formula
 
  • #4
f(police) = v / (v + v(source)) *f(source)

440 = 494 (767 / (767 + v))

v= 94 mph

does this make sense?
 
  • #5
Actually, f(source) = 440 Hz & f(observer) = 494 Hz, so you'll get -94 mph.
 
  • #6
The correct answer is 83 mph.
 
  • #7
Yeah, I didn't look up the Doppler effect formula, but I thought about it for a few minutes and came up with the following for a stationary observer and moving source:

[tex] f = f_0\left[\frac{1}{1 + v/c_s}\right] [/tex]

where cs is the sound speed, v is the source speed relative to the observer, and I use the convention that:
v > 0 if the source moves away from the observer and,
v < 0 if the source moves toward the observer.

It makes sense at least to the extent that f > f0 for v < 0 and vice versa.

Using this formula, with a sound speed of 343.2 m/s (taken from Wikipedia for dry air at 20 C) I get a result of:

v = -83.9 mi/h
 
Last edited:

Related to Doppler effect car horn question

1. What is the Doppler effect and how does it relate to a car horn?

The Doppler effect is the change in frequency or pitch of a sound wave due to the relative motion between the source of the sound and the observer. In the case of a car horn, as the car approaches, the sound waves are compressed, resulting in a higher frequency or pitch. As the car moves away, the sound waves are stretched, resulting in a lower frequency or pitch.

2. Why does a car horn sound different when it is approaching versus when it is moving away?

The change in frequency of a sound wave due to the Doppler effect causes the car horn to sound different when approaching versus moving away. As the car approaches, the frequency of the sound waves increases, resulting in a higher pitch. As the car moves away, the frequency decreases, resulting in a lower pitch.

3. How does the speed of the car affect the Doppler effect on a car horn?

The speed of the car directly affects the Doppler effect on a car horn. The faster the car is moving, the greater the change in frequency of the sound waves. This means that the pitch of the car horn will sound higher when the car is approaching and lower when the car is moving away at a faster speed.

4. Does the Doppler effect only occur with sound waves?

No, the Doppler effect can occur with any type of wave, including light waves. This is why we see a shift in the color of stars as they move closer or further away from us. However, the Doppler effect is more noticeable with sound waves because we can perceive changes in pitch more easily than changes in light.

5. Can the Doppler effect be observed with stationary objects?

No, the Doppler effect only occurs when there is relative motion between the source of the sound and the observer. If both the source and the observer are stationary, there will be no change in frequency or pitch of the sound waves, and therefore no Doppler effect.

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