Answer:
C) 21 m/s
Explanation:
The general formula of the Doppler effect is:
[tex]f'=(\frac{v+v_r}{v+v_s})f[/tex]
where
f' is the apparent frequency
f is the original frequency
v is the speed of the wave in the medium
[tex]v_r[/tex] is the velocity of the receiver, positive if the receiver is moving towards the source
[tex]v_s[/tex] 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
[tex]v_r = 0[/tex] (the observer is stationary)
[tex]v_s[/tex] 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
[tex]f'=(\frac{v}{v+v_s})f[/tex]
And solving for [tex]v_s[/tex], we find the speed of the train
[tex]v_s = v(\frac{f}{f'}-1)=(343 m/s)(\frac{440 Hz}{415 Hz}-1)=20.7 m/s \sim 21 m/s[/tex]
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).
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.
Mathematically, Doppler's effect of a wave is given by this formula:
[tex]F_o = \frac{V+V_r}{V+V_s}F[/tex]
Substituting the given parameters into the formula, we have;
[tex]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[/tex]
Speed = 20.66 ≈ 21 m/s.
Read more on Doppler's effect here: brainly.com/question/3841958
