A and B are two sources generating sound waves. A listener is situated at C . The frequency of the source at A is 500 ~Hz . A, now, moves towards C with a speed 4 ~m / s . The number of beats heard at C is 6 . When A

JEE Main 201322 AprilOnline

JEE Main 2013 · 22 April · Online · Physics · Waves and Sound

A and B are two sources generating sound waves. A listener is...

A and B are two sources generating sound waves. A listener is situated at

\mathrm{C}

. The frequency of the source at

\mathrm{A}

500 \mathrm{~Hz}

. A, now, moves towards

\mathrm{C}

with a speed

4 \mathrm{~m} / \mathrm{s}

. The number of beats heard at

\mathrm{C}

is 6 . When

\mathrm{A}

moves away from

C

with speed

4 \mathrm{~m} / \mathrm{s}

, the number of beats heard at

\mathrm{C}

is 18 . The speed of sound is

340 \mathrm{~m} / \mathrm{s}

. The frequency of the source at

\mathrm{B}

is :

C. $512 \mathrm{~Hz}$

\mathrm{f}=500 \mathrm{ Hz}

Case 1: When source is moving towards stationary listener apparent frequency

\eta^{\prime}=\eta \left(\frac{\mathrm{v}}{\mathrm{v}-\mathrm{v}_{\mathrm{s}}}\right) =500\left(\frac{340}{336}\right)=506 \mathrm{ Hz} Case 2 : When source is moving away from the stationary listener \eta^{\prime \prime}=\eta\left(\frac{\mathrm{v}}{\mathrm{v}+\mathrm{v}_{\mathrm{s}}}\right)=500\left(\frac{340}{344}\right)=494 \mathrm{ Hz} In case 1 number of beats heard is 6 and in case 2 number of beats heard is 18 therefore frequency of the source at \mathrm{B}=512 \mathrm{ Hz}