Question

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 32 m/s and accelerating at 1.1 m/s2. A train is approaching you from the opposite direction on the other track at 40 m/s, accelerating at 1.5 m/s2, and sounds its whistle, which has a frequency of 460 Hz. At that instant, what is the perceived frequency that you hear? (Round your answer to one decimal place.)

Answer 1

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

370.9 Hertz

The function is given as:

`f_(o)=(c+V_(o) )/(c-V_(o) )` x
`f_(s)`

From the question

`c=332` --- speed of the sound

`V_(o) =32` ---current speed of the train

`V_(s) = 40` --- speed of the opposite train

`f_(s) =460` --- frequency of the sound wave

This gives:

`f_(o)= (332-32)/(332+40)` ×
`460`

`f_(o)= (300)/(372) x460`

Rewrite as:

`f_(o)= (300x460)/(372)`

`f_(o)= 370.9`

Answer 2

Doppler Effect happens when there is shift in frequency during a realtive motion between a source and the observer of that source.

It can be calculated as:

`f_o=f_s\huge \text((c+v_o)/(c+v_s)\huge \text )`

where:

c is the speed of light (c = 332m/s)

all the subscripted s is related to the Source (frequency, velocity);

all the subscripted o is related to the Observer (frequency, velocity);

As the source is moving towards the observer and the observer is moving towards the source, the velocities of each are opposite related to direction.

So, the frequency perceived by the observer:

`f_o=460\huge \text((332+32)/(332-40)\huge \text)`

`f_o=460\huge \text((364)/(292)\huge \text)`

`f_o=460(1.247)`

`f_o= 573.6 \ \text{Hz}`

At this condition, the observer hears the train's horn in a perceived frequency of 573.6 Hz