Physics Question.?

Question

Describe how a person, at rest, with a source of sound (perhaps a speaker emitting a single frequency) can determine the velocity of an object moving toward the person by measuring the frequency of the sound reflected back to the person from the moving object.

Answer 1

Doppler 's shift or Doppler's effect

The speed of acoustical wave in the medium is constant )(it is about 332 m/s in the air)
v=lf
v- speed of the wave
l - wave length
f frequency
Since speed of propagation is constant the frequency will change.

The frequency of the wave that travel through a medium by:

f'=[v/(v+vs)] f
where
v - the speed of waves in the medium
vs - the velocity of the source (the thing emitting the sound)

The sound will travel to the incoming object and will bounce off with frequency

f1=[v/(v+vs)] f0

However the person would hear

f2=[v/(v+vs)] f1
f2 =[v/(v+vs) [v/(v+vs)f0

f2 =f0 [v/(v+vs)]^2

Answer 2

Doppler effect provides the answer.
The person acts as listener at rest ,the moving object acts as mirror to reflect sound.(If speed of image in mirror is v then speed of mirror (object ) is v/2.(THE IMAGE FORMED ACTS AS SOURCE)
reflected (apparent) frequency=true frequency{c /( c-v)}
where 'c' is velocity of sound in air and velocity of moving object is v /2

Answer 3

♠ suppose you are sitting between source of the sound with frequency f0 and reflector moving to you with speed u;
the one who is sitting on reflector will register frequency f1=f0(1+u/c), where c is speed of sound in the air;
now since reflector is moving to you you will also register frequency f2=f1(1+u/c);
♣ thus f2= f0(1+u/c)^2, hence sqrt(f2/f0) = 1+u/c, hence u=(sqrt(f2/f0) –1)*c;
negative u means the reflector is moving from you;