Determining the Speed of a Car from Skid MarksHow fast was the car going?

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In summary, the person heard a 546 Hz whistle being blown from close by and the frequency of the whistle dropped as the train passed by. The frequency of the train at rest was 469 Hz. The best equation I could come up with to calculate the speed of the train is 340 m/s.
  • #1
BooGTS
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Problem goes as follows:

A person standing close to a railroad crossing hears the whistle of an approaching train. He notes that the pitch of the whistle drops as the train passes by and moves away from the crossing. The frequency of the distant approaching whistle is 546 Hz; it drops to 469 Hz after the train is well past the crossing. What is the speed of the train? Use 340 m/s for the speed of sound in air.

Hint: Calculate the ratio of frequency of the whistle before and after the crossing. That ratio does not include the frequency of the train at rest.

The best I've been able to come up with is:

546 Hz=507.5 Hz (340 m/s/(340 m/s-X))
1.076=(340/(340-X))
1.076(340-X) = 340
365.8 - 1.076X = 340
-1.076X = - 25.8
X=23.97 m/s

Any suggestions?
 
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  • #2
BooGTS said:
Problem goes as follows:

A person standing close to a railroad crossing hears the whistle of an approaching train. He notes that the pitch of the whistle drops as the train passes by and moves away from the crossing. The frequency of the distant approaching whistle is 546 Hz; it drops to 469 Hz after the train is well past the crossing. What is the speed of the train? Use 340 m/s for the speed of sound in air.

Hint: Calculate the ratio of frequency of the whistle before and after the crossing. That ratio does not include the frequency of the train at rest.

The best I've been able to come up with is:

546 Hz=507.5 Hz (340 m/s/(340 m/s-X))
1.076=(340/(340-X))
1.076(340-X) = 340
365.8 - 1.076X = 340
-1.076X = - 25.8
X=23.97 m/s

Any suggestions?

You cannot assume that the frequency of the whistle is midway between the two frequencies given to you! It is not!
You must treat the frequency of the whistle as being an unknown. Write the equation for the Doppler effect when the source is moving toward the observer (and the frequency observed is 546 Hz) and then the equation when it is moving away (with the frequency observed 469 Hz). That will give you two equations with two unknowns (the speed of the train and the frequency of the whistle.) If you take the ratio of the two equations the frequency of the whistle will cancel out.
 
  • #3
Thanks nrqed,

Thats basically what the hint said, but it helped. Here is the finished problem:

((340/340-Vs)*((340+Vs/340)) = 1.164

(115600+340Vs)/(115600-340Vs) = 1.164

115600+340Vs = 1.164 (115600-340Vs)

115600+735.76Vs = 134558.4

735.76Vs = 18958.4

=25.77 m/s


I have one more problem that I could use some help on, I'll bump it to the top ;)
 

What is the frequency of sound?

The frequency of sound refers to the number of complete vibrations or cycles that occur in a second. It is measured in hertz (Hz), with one hertz being equal to one vibration per second.

What factors affect the speed of sound?

The speed of sound is affected by several factors, including the medium through which it travels (such as air, water, or solid materials), temperature, and density. In general, sound travels faster in denser mediums and at higher temperatures.

What is the speed of sound in air?

The speed of sound in air is approximately 343 meters per second at room temperature and sea level. However, this can vary depending on factors such as humidity and air pressure.

How does the frequency of sound affect pitch?

The frequency of sound is directly related to the pitch we perceive. Higher frequencies correspond to higher pitches, while lower frequencies correspond to lower pitches. For example, a guitar string vibrating at a higher frequency produces a higher-pitched sound than a string vibrating at a lower frequency.

Can sound travel through a vacuum?

No, sound cannot travel through a vacuum because there is no medium for the sound waves to propagate through. Sound waves require particles to vibrate in order to travel, and in a vacuum, there are no particles present.

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