The equation for the Doppler shift of a sound wave of speed v, reaching a moving detector, is where vd is the speed of the detector; vs is the speed of the source; f is the frequency of the source; f' is the frequency at the detector. If the detector moves toward the source, vd is positive; if the source moves toward the detector, vs if positive. A train moving toward a detector at 35 m/s blows a 303-Hz horn. What frequency is detected by a (a) stationary train

Given Information:

Speed of train = vs = 35 m/s

Frequency of horn = fs = 303 Hz

Speed of sound = v = 340 m/s

Required Information:

Frequency detected = fd = ?

Answer:

Frequency detected = fd ≈ 338 Hz

Explanation:

The Doppler effect is the increase or decrease in the observed frequency of a wave when the source or the observer move relative to each other.

The equation of Doppler effect is given by

fd = fs * (v ± vd) / (v ± vs)

Where fs is the frequency of horn, vs is the speed of train and v is the speed of light.

Since the source is moving towards the detector, vs will be negative and detector is stationary therefore, vd = 0

fd = fs * (v - 0) / (v - vs)

fd = 303 * (340/340-35)

fd ≈ 337.77 Hz

fd ≈ 338 Hz

Therefore, the frequency detected by stationary detector is 338 Hz.