An approaching train produces the RP1 signal (attention signal) at 600 Hz . The train moves with the speed of 120 km. What is the frequency and the wavelength of the sound
detected by a person standing next to the track?
See previous post: 5-5-14, 11:42 AM.
To calculate the frequency and wavelength of the sound detected by a person standing next to the track, we need to consider the Doppler effect. The Doppler effect describes the change in frequency and wavelength of a wave as a result of relative motion between the source of the wave (in this case, the approaching train) and the observer (the person standing next to the track).
The formula for the Doppler effect is as follows:
f' = (v + v_o) / (v + v_s) * f
Where:
f' = observed frequency
f = actual frequency
v = speed of sound
v_o = observer's velocity relative to the medium
v_s = source's velocity relative to the medium
In this case, the relative speed of the train is the sum of the speed of the train (given as 120 km/hr) and the speed of sound (approximately 343 m/s). Since the observer is stationary, the observer's velocity relative to the medium is 0.
Given:
Actual frequency (f) = 600 Hz
Speed of sound (v) = 343 m/s
Speed of train (v_s) = 120 km/hr
First, convert the speed of the train from km/hr to m/s:
Speed of train (v_s) = 120 km/hr * (1000 m/1 km) * (1 hr/3600 s) = 33.33 m/s (rounded to two decimal places)
Now, substitute these values into the Doppler effect formula to find the observed frequency (f'):
f' = (343 m/s + 0 m/s) / (343 m/s + 33.33 m/s) * 600 Hz
f' = 343 m/s / 376.33 m/s * 600 Hz
f' = 548.21 Hz (rounded to two decimal places)
Therefore, the frequency of the sound detected by a person standing next to the track is approximately 548.21 Hz.
To find the wavelength, we can use the formula:
wavelength = v / f'
Substituting the values we already know:
wavelength = 343 m/s / 548.21 Hz
wavelength ≈ 0.626 meters (rounded to three decimal places)
Therefore, the wavelength of the sound detected by a person standing next to the track is approximately 0.626 meters.