1
Question
In above shown figure a car and a fire truck both are moving towards each other. A man is standing on the sidewalk to the left the car, and a woman is standing on the sidewalk to the right of the truck. The truck starts its siren and the truck driver, the car driver, the man and the woman all hear the
siren as having a different pitch. Which of the following lists the
people in order by the pitch they hear, from lowest pitch to highest
pitch?
In above shown figure a car and a fire truck both are moving towards each other. A man is standing on the sidewalk to the left the car, and a woman is standing on the sidewalk to the right of the truck. The truck starts its siren and the truck driver, the car driver, the man and the woman all hear the
siren as having a different pitch. Which of the following lists the
people in order by the pitch they hear, from lowest pitch to highest
pitch?
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Solution
The correct option is B Woman, truck driver, man, car driver
As there is a relative motion between source of sound and observer, therefore, Doppler's effect comes into play let f=original frequency of sound , v=velocity of sound in air, vo=velocity of observer , vs=velocity of source , f′=apparent frequency of sound
When car driver observes the siren he will receive the frequency f′=f(v+vov−vs) .....eq1 , gives that f′>f because v+v0>v−vs where , source and observer both are approaching each other When man observes the siren he will receive the frequency f′=f(vv−vs) .......eq2 gives that f′>f because v>v−vs by above two equations we get f′>f but in eq1 the numerator is greater than the numerator in eq2 , therefore car driver observes greater frequency than standing manwhere , source is approaching the observer and observer is at rest
When woman observes the siren she will receive the frequency f′=f(vv+vs) ...........eq3 gives that f′<f because v<v−vs where , source is going away from observer and observer is at rest
When truck driver observes the siren he will receive the frequency f′=f(vv)=f .............eq4where, source and observer both are moving in the same direction with same velocity
As there is a relative motion between source of sound and observer, therefore, Doppler's effect comes into play
let f=original frequency of sound ,
v=velocity of sound in air,
vo=velocity of observer ,
vs=velocity of source ,
f′=apparent frequency of sound
When car driver observes the siren he will receive the frequency f′=f(v+vov−vs) .....eq1 , gives that f′>f because v+v0>v−vs
where , source and observer both are approaching each other
When man observes the siren he will receive the frequency
f′=f(vv−vs) .......eq2 gives that f′>f because v>v−vs
by above two equations we get f′>f but in eq1 the numerator is greater than the numerator in eq2 , therefore car driver observes greater frequency than standing man
where , source is approaching the observer and observer is at rest
When woman observes the siren she will receive the frequency
f′=f(vv+vs) ...........eq3 gives that f′<f because v<v−vs
where , source is going away from observer and observer is at rest
When truck driver observes the siren he will receive the frequency
f′=f(vv)=f .............eq4
where, source and observer both are moving in the same direction with same velocity
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