If a sound with frequency fs is produced by a source traveling along a line with speed vs. If an observer is traveling with speed vo along the same line from the opposite direction toward the source, then the frequency of the sound heard by the observer is fo = c + vo c − vs fs where c is the speed of sound, about 332 m/s. (This is the Doppler effect.) Suppose that, at a particular moment, you are in a train traveling at 42 m/s and accelerating at 1.2 m/s2. A train is approaching you from the opposite direction on the other track at 47 m/s, accelerating at 1.7 m/s2, and sounds its whistle, which has a frequency of 441 Hz. At that instant, what is the perceived frequency that you hear? (Round your answer to one decimal place.)

vs = velocity of source relative to observer = - 47 m/s ( the negative sign is as a result of the fact that the velocity of the source is in opposite direction to the observer).

fs = frequency of sound wave by source = 441 Hz

By substituting the parameters, we have

fo = 332 + 42/ 332 - (-47) × 441

fo = (374/ 332 + 47) × 441

fo = (373/ 379) × 441

fo = 0.9841 × 441

fo = 434.02 Hz

chibuikeumeh chibuikeumeh · Answer 2 · 2021-10-24T18:58:20+02:00

The perceived frequency of sound is the amount of sound wave that pass a point in a given amount of time

The perceived frequency you hear is 337.4 Hertz

The function is given as:

[tex]\mathbf{f_o = \frac{c + v_o}{c - v_s} \times f_s}[/tex]

From the question

[tex]\mathbf{c = 332}[/tex] --- speed of the sound

[tex]\mathbf{v_o = 42}[/tex] ---current speed of the train

[tex]\mathbf{v_s = -47}[/tex] --- speed of the opposite train

[tex]\mathbf{f_s = 441}[/tex] --- frequency of the sound wave

So, we have:

[tex]\mathbf{f_o = \frac{c + v_o}{c - v_s} \times f_s}[/tex]

This gives:

[tex]\mathbf{f_o = \frac{332 - 42}{332 +47} \times 441}[/tex]

[tex]\mathbf{f_o = \frac{290}{379} \times 441}[/tex]

Rewrite as:

[tex]\mathbf{f_o = \frac{290\times 441}{379} }[/tex]

[tex]\mathbf{f_o = 337.4}[/tex]

The perceived frequency you hear is 337.4 Hertz