A stationary horn emits a 151 Hz tone. What frequency is heard by a passenger on a train which is moving towards this horn with a speed of 28.7 m/s?
To determine the frequency heard by the passenger on the moving train, we need to consider the concept of the Doppler effect. The Doppler effect describes the change in frequency or pitch observed when there is relative motion between a source of sound and an observer.
The formula for the observed frequency, \(f_{\text{obs}}\), is given by:
\[f_{\text{obs}} = \frac{(v + v_o)}{(v + v_s)} \cdot f_s\]
where \(v\) is the speed of sound, \(v_o\) is the velocity of the observer, \(v_s\) is the velocity of the source of sound, and \(f_s\) is the frequency of the source of sound.
In this case, the source of sound is the stationary horn with a frequency of 151 Hz. The observer is the passenger on the moving train with a velocity of 28.7 m/s. We can assume the speed of sound is \(v = 343 \, \text{m/s}\) in air at room temperature.
Plugging in the values into the formula, we get:
\[f_{\text{obs}} = \frac{(343 + 0)}{(343 + 28.7)} \cdot 151\]
Simplifying the equation:
\[f_{\text{obs}} = \frac{343}{371.7} \cdot 151\]
\[f_{\text{obs}} \approx 139.4 \, \text{Hz}\]
Therefore, the frequency heard by the passenger on the moving train is approximately 139.4 Hz.
Fh = 151 Hz
Vr = 28.7 m/s
Vs = 343 m/s
Fr = ((Vs+Vr)/(Vs-Vh)) * Fh
Fr = ((343+28.7)/(343-0)) * 151 Hz =
(371.7/343) * 151 = 163.6 Hz = Freq.
heard by the receiver(Passenger).