How Does the Doppler Effect Alter Wavelength as a Train Approaches?

[astronomystudent]

1.) Suppose the sound from an approaching train whistle normally has a frequency of 1200 cycles per second, but the train is approaching at 50 meters per second. How would the Doppler Effect change the wavelength of the sound? (speed of sound 335 meters per second; I would like a quantitative answer here for full credit)

So far I have done the following: c = wavelength (frequency)
335 = wavelength (1200)
335/1200 = wavelength
wavelength = .279
wavelength = 2.79 x 10^-1 meters

c = wavelength (frequency)
335 = wavelength (1200 + 50)
335/1250 = wavelength
wavelength = .268
wavelength = 2.7 x 10^-1 meters

These are the forumlas I have from class, but I don't know any other way to solve the problem or if it is right.

 

[Nate810]

The Doppler Effect would change the wavelength of the sound from 2.79 x 10^-1 meters to 2.7 x 10^-1 meters.

 

[kyle8921]

The Doppler Effect is a phenomenon that occurs when there is relative motion between a source of waves (in this case, the train) and an observer. It results in a change in the frequency and wavelength of the waves perceived by the observer.

To solve this problem, we can use the formula for the Doppler Effect: f' = f(v + vr)/v, where f' is the perceived frequency, f is the actual frequency, v is the speed of sound, and vr is the relative velocity between the source and the observer.

In this case, the source (train) is approaching the observer, so the relative velocity is positive. We can plug in the given values: f = 1200 cycles per second, v = 335 meters per second, and vr = 50 meters per second.

f' = (1200)(335 + 50)/335 = 1340 cycles per second

This means that the perceived frequency of the train whistle will be 1340 cycles per second instead of the actual 1200 cycles per second. To find the wavelength, we can use the formula c = f'λ, where c is the speed of sound and λ is the wavelength.

λ = c/f' = (335 meters per second)/(1340 cycles per second) = 0.25 meters

Therefore, the wavelength of the sound from the approaching train will be 0.25 meters, which is shorter than the original wavelength of 0.279 meters. This is because the perceived frequency is higher due to the Doppler Effect.