Question

16
A source of sound s. starts moving with a constant speed v along the circumference of a circle of radius
R

(RO)

Dis a detector fixed on X-axis
Find the time at which the detector detects sound of highest frequency for the 1st time
​

Answer 1

Answer:

In this kind of question, you need to apply Concept of Doppler Effect .ax apparent frequency is observed when the direction of velocity of sound is towards the observer.

In a circular trajectory , it's possible to have such a case only as a tangent from the source to that point.

In the triangle ACD

${2R}^{2} = {R}^{2} + {x}^{2}$

$= > x = R \sqrt{3}$

Now let's try to find angle ACD :

$\angle ADC = { \tan}^{ - 1} \bigg(\dfrac{ \cancel R}{ \cancel R \sqrt{3} } \bigg) = 30 \degree$

So angle ACD = 90°-30° = 60°

So angle ACE = 90° - ACD = 30°

So from the starting position , this tangent position is obtained after :

180° + 30° = 210 ° ..........(1)

So the arc will be 210/360 = 7/12 th part of a full circle .

So time to be taken :

$t = \dfrac{distance}{speed}$

$= > t = \dfrac{ \frac{7}{12} (2\pi R)}{v}$

$= > t = \dfrac{7\pi R}{6v}$

So final answer :

$\boxed{ \blue{ \bold{ \huge{t = \dfrac{7\pi R}{6v} }}}}$

Answer 2

The above diagram shows the figure.

Concept Used : Doppler's Effect

$</p><p></p><p>\tt{\purple {\implies{t\:= \dfrac{Speed}{Distance} }}}$

$\tt {\red {\implies { t = \dfrac{ \frac{7}{12} (2\pi R)}{v} }}}$

$</p><p>\tt {\blue{ \implies{ t = \dfrac{7\pi R}{6v} }}}..........(A)$