A small source of sound moves on a circle as shown in the figure and an observer is standing on $O$ . Let $n_{1}$ , $n_{2}$ and $n_{3}$ be the frequencies heard when the source is at $A, B$ and $C$ respectively. Then

n_{1} > n_{2} > n_{3}

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n_{2} > n_{1} > n_{3}

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n_{1} = n_{2} > n_{3}

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n_{2} > n_{3} > n_{1}

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Solution

The correct option is D $n_{2} > n_{3} > n_{1}$

Let $n_{1}$ , $n_{2}$ and $n_{3}$ be the frequencies heard when the source is at $A$ , $B$ and $C$ respectively and an observer is standing on $O$ .

From Doppler effect the apparent frequency heard by the observer,
$n_{1} = n (\frac{v + v_{0}}{v \mp v_{s}})$

$n =$ actual frequency of the sound,
$v =$ speed of sound in medium,
$v_{0} =$ speed of observer,
$v_{s} =$ speed of source,

At point $A$ , source is moving away from observer, so the apparent frequency
$n_{1} = n (\frac{v}{v + v_{s}})$

which is less than actual frequency $(n)$ .
$n_{1} < n$

At point $B$ , source is moving towards the observer, so the apparent frequency
$n_{2} = n (\frac{v}{v - v_{s}})$

which is more than actual frequency $(n)$ .
$n_{2} > n$

At point $C$ , source is moving perpendicular to the observer, so the apparent frequency is little higher than actual frequency but less than point $B$ .
$n_{3} = n$

Therefore, the combined result of these three statements are expressed as,

$n_{2} > n_{3} > n_{1}$

Final answer: (b)

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Similar questions

Q. A small source of sounds moves on a circle as shown in figure (16-Q1) and an observer is sitting at O. Let

v_{1}, v_{2}, v_{3}

be the frequencies heard when the source is at A, B and C respectively.
(a)

v_{1} > v_{2} > v_{3}

(b)

v_{1} = v_{2} > v_{3}

(c)

v_{2} > v_{3} > v_{1}

(d)

v_{1} > v_{3} > v_{2}

Q. A small source of sound moves on a circle as shown in fig. and an observer is sitting at

O

. Let at

v_{1}, v_{2}, v_{3}

be the frequencies heard when the source is at

A, B

and

C

respectively.

A small source of sound S of frequency 500 Hz is attached to the end of a light string and is whirled in a vertical circle of radius 1.6 m. The string just remains tight when the source is at the highest point. (a) An observer is located in the same vertical plane at a large distance and at the same height as the centre of the circle (figure 16-E13). The speed of sound in air $= 330 m s^{- 1}$ and $g = 10 m s^{- 2}$ . Find the maximum frequency heard by the observer. (b) An observer is situated at a large distance vertically above the centre of the circle. Find the frequencies heard by the observer corresponding to the sound emitted by the source when it is at the same height as the centre.