JEE Advanced · 2023 · 04 Jun 2023 · Paper 2 · Waves & Sound

Passage

S_{1}

and

S_{2}

are two identical sound sources of frequency 656 Hz . The source

S_{1}

is located at

O

and

S_{2}

moves anti-clockwise with a uniform speed

42 ms^{- 1}

on a circular path around

O

, as shown in the figure. There are three points

P, Q

and

R

on this path such that

P

and

R

are diametrically opposite while

Q

is equidistant from them. A sound detector is placed at point

P

. The source

S_{1}

can move along direction

O P

.
[Given: The speed of sound in air is

324 ms^{- 1}

]

S_{1}

and

S_{2}

are two identical sound sources of frequency 656 Hz. The source

S_{1}

is located at

O

and

S_{2}

moves anti-clockwise with a uniform speed

42 ms^{- 1}

on a circular path around

O

, as shown in the figure. There are three points

P, Q

and

R

on this path such that

P

and

R

are diametrically opposite while

Q

is equidistant from them. A sound detector is placed at point

P

. The source

S_{1}

can move along direction

O P

.
[Given: The speed of sound in air is

324 ms^{- 1}

]

When only

S_{2}

is emitting sound and it is at

Q

, the frequency of sound measured by the detector in Hz is ____.

Answer: 648

Solution

At point Q, the velocity of

S_{2}

makes an angle of 45° with the line QP.

The component of velocity along QP is:

v_{radial} = 42 cos (45°) = 42 \times \frac{1}{2} = 4

m/s.

Since

S_{2}

is moving away from P, the observed frequency is:

f^{'} = \frac{c}{c + v _{radial}} f = \frac{324}{324 + 4} \times 656 = \frac{324}{328} \times 656 = 648

Hz.

JEE Advanced · 2023 · 04 Jun 2023 · Paper 2 · Numerical answer