Question

A train moving at a constant speed is passing a stationary observer on a platform. On one of the train cars, a flute player is continually playing the note known as concert A (f = 440 Hz). After the flute has passed, the observer hears the sound with a frequency of 415 Hz. What is the speed of the train? The speed of sound in air is 343 m/s. A) 7.3 m/s B) 12 m/s C) 21 m/s D) 37 m/s E) 42 m/s

Answer 1

Answer:

C) 21 m/s

Explanation:

The general formula of the Doppler effect is:

$f'=(\frac{v+v_r}{v+v_s})f$

where

f' is the apparent frequency

f is the original frequency

v is the speed of the wave in the medium

$v_r$ is the velocity of the receiver, positive if the receiver is moving towards the source

$v_s$ is the velocity of the source, positive if the source is moving away from the receiver

Here we have

f = 440 Hz

f' = 415 Hz

v = 343 m/s

$v_r = 0$ (the observer is stationary)

$v_s$ is positive since we are considering when the train has passed the observer, so it is moving away from him

So we can rewrite the formula as

$f'=(\frac{v}{v+v_s})f$

And solving for $v_s$, we find the speed of the train

$v_s = v(\frac{f}{f'}-1)=(343 m/s)(\frac{440 Hz}{415 Hz}-1)=20.7 m/s \sim 21 m/s$

Answer 2

By applying Doppler's effect of a wave, the speed of this train is equal to 21 m/s.

Given the following data:

Maximum frequency = 440 Hz.

Apparent frequency = 415 Hz.

Speed of sound in air = 343 m/s.

Observer speed = 0 m/s (since his stationary).

What is Doppler effect?

Doppler effect can be defined as the change in frequency of a wave with respect to an observer that is in motion and moving relative to the source of the wave.

How to calculate the speed of the train.

Mathematically, Doppler's effect of a wave is given by this formula:

$F_o = \frac{V+V_r}{V+V_s}F$

Substituting the given parameters into the formula, we have;

$415 = \frac{343+0}{343+V_s} \times 440\\\\142345+415V_s=150920\\\\415V_s=150920-142345\\\\415V_s=8575\\\\V_s=\frac{8575}{415} \\\\V_s=20.66$

Speed = 20.66 ≈ 21 m/s.

Read more on Doppler's effect here: brainly.com/question/3841958