Question

You are at a railroad crossing waiting for a freight train traveling at a speed of 22.8 m/s to pass by. The frequency of the train's horn is 325 Hz. (Use 343 m/s as the speed of sound.)

(a) Determine the overall change in frequency you detect as the train moves from approaching to receding. Use the sign of your answer to indicate whether the frequency increases or decreases.(b) Determine the overall change in wavelength you detect as the train moves from approaching to receding. Use the sign of your answer to indicate whether the wavelength increases or decreases.

Answer 1

Answer: a) -43.4 Hz, b) -7.90m

Explanation: This is a question under Doppler effect.

The mathematical equation of doppler effect is given as

fo = (v + vo)/(v -vs) × fs

Where fo = frequency perceived by observer = ?

v = speed of sound in air = 343m/s

vo = velocity of obseerver relative to the source = 0 (since he is not moving)

vs = velocity of source relative to the observer = 22.8 m/s

fs = frequency of sound produced by source = 325 Hz

For the condition where the train is approaching the observer, velocity of source relative to the observer (vs) is positive, hence vs = 22.8 m/s

fo = (343+0)/(343 -22.8) × 325

fo = (343/ 320.2) × 325

fo = 1.071 × 325 = 348.14 Hz.

For the condition where the train is moving away from the observer, velocity of source relative to the observer (vs) is negative, hence vs = -22.8 m/s

fo = (343+0)/(343 -(-22.8)) × 325

fo = (343/ 343 +22.8) × 325

fo = (343/365.8) × 325

fo = 0.9377 × 325 = 304.74 Hz

Change in frequency as the train moves from approaching to receeding is = 304.74 - 348.14 = -43.4 Hz.

But v = speed of sound in air = 343 m/s.

We can get the change in wavelength by using the formulae

V = fλ

Where v = speed of sound in air = 343 m/s

f = change in frequency = -43.4 Hz

λ = change in wavelength = ?

343 = (-43.4) × λ

λ = 343 / -43.4

λ = -7.90 m

The negative sign beside the wavelength shows decrease