A whistle ' S ' of frequency f revolves in a circle of radius R at a constant speed v . rati

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14.Waves and Sound

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A whistle ' $S$ ' of frequency $f$ revolves in a circle of radius $R$ at a constant speed $v$. What is the ratio of maximum and minimum frequency detected by a detector $D$ at rest at a distance $2 R$ from the center of circle as shown in figure? (take ' $c$ ' as speed of sound)

A

$\left(\frac{c+v}{c-v}\right)$

B

$\sqrt{2}\left(\frac{c+v}{c-v}\right)$

C

$\sqrt{2}$

D

$\frac{(c+v)}{c \sqrt{2}}$

Solution

(a)

$c=$ Speed of sound

At maximum frequency sources directly approaches observes with speed $v_{ s }$.

$\therefore f_{ A }=\frac{c}{c-v} f_0$

At minimum frequency sources recedes with $v_{ s }$

$f_R=\frac{c}{c+v} f_0$

$\frac{f_A}{f_R}=\frac{c+v}{c-v}$

Standard 11

Physics

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