An approaching train produces the RP1 signal (attention signal) at 600 Hz . The train moves with the speed of 120 km/h. What is the frequency and the wavelength of the sound
detected by a person standing next to the track?
Vt=120000m/h = 120000m/3600s = 33.33 m/s
Fp = ((Vs+Vp)/(Vs-Vt))*Ft
Fp = ((343+0)/(343-33.33))*600 Hz
Fp = (343/309.7)*600 = 664.6 Hz = Freq.
heard by the person.
L = Vs/Fp = 343/664.6 = 0.516 m. = Wave-
length.
To find the frequency and the wavelength of the sound detected by a person standing next to the track, we need to use the Doppler effect formula. The Doppler effect is the change in frequency or wavelength of a wave observed by an observer moving relative to the source of the waves.
The formula for the Doppler effect is given by:
f' = (v + vr) / (v + vs) * f
where:
- f' is the observed frequency
- v is the speed of sound in air (approximately 343 m/s)
- vr is the velocity of the receiver (person standing next to the track)
- vs is the velocity of the source (the speed of the train)
- f is the emitted frequency (600 Hz in this case)
To find the observed frequency (f'), we need to know the values of vr and vs. Given that the train moves at 120 km/h, we need to convert this to m/s by dividing by 3.6:
vs = 120 km/h ÷ 3.6 = 33.33 m/s
The velocity of the receiver (vr) is assumed to be 0, as the person is standing next to the track (not moving towards or away from the track).
Using the values in the formula, we can calculate the observed frequency (f'):
f' = (343 + 0) / (343 + 33.33) * 600 Hz
f' = 343 / 376.33 * 600 Hz
f' ≈ 546.24 Hz
Therefore, the observed frequency of the sound detected by the person standing next to the track is approximately 546.24 Hz.
To find the wavelength, we can use the formula:
wavelength = v / f'
where v is the speed of sound in air.
wavelength = 343 m/s / 546.24 Hz
wavelength ≈ 0.628 m
Therefore, the wavelength of the sound detected by the person standing next to the track is approximately 0.628 meters.