A train blows its horn as it approaches a crossing. The train engineer observes a frequency of 118 Hz and a stationary observer observes a frequency of 122 Hz. What is the speed of the train? Use the speed of sound as 340m/sec
Fo = ((Vs+Vo)/(Vs-Vt))*Ft = 122 Hz
((340+0)/(340-Vt))*118 = 122
(340/(340-Vt))*118 = 122
40,120/(340-Vt) = 122
41,480-122Vt = 40,120
-122Vt = 40,120 - 41,480 = -1360
Vt = 11.15 m/s. = Velocity of the train.
To solve this problem, we can use the formula for the Doppler effect. The Doppler effect is the change in frequency of a wave for an observer moving relative to the source of the wave.
The formula for the Doppler effect is given as:
f' = f * (v + v₀) / (v + vₛ)
Where:
- f' is the observed frequency
- f is the actual frequency emitted by the source
- v is the speed of sound in the medium (in this case, 340 m/s)
- v₀ is the speed of the observer relative to the medium
- vₛ is the speed of the source of the sound
In this case, the frequency observed by the stationary observer is 122 Hz, the frequency observed by the train engineer is 118 Hz, and the speed of sound is 340 m/s.
To find the speed of the train (vₛ), we can rearrange the formula as follows:
vₛ = v * (f' - f) / (f' + f)
Substituting the given values:
vₛ = 340 * (122 - 118) / (122 + 118)
vₛ = 340 * 4 / 240
vₛ = 5.67 m/s
Therefore, the speed of the train is approximately 5.67 m/s.