JEE Main · 2022 · 28 Jun 2022 · Shift 1 · Waves & Sound

The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be:

Answer: (D)

Solution

The beat frequency is

f_{b} = \frac{40}{12} = \frac{10}{3}

Hz. For sound waves,

f = \frac{v}{λ}

, so the beat frequency is

f_{b} = f_{1} - f_{2} = \frac{v}{λ _{1}} - \frac{v}{λ _{2}} = v (\frac{1}{4.08} - \frac{1}{4.16})

. Solving:

\frac{10}{3} = v (\frac{4.16 - 4.08}{4.08 \times 4.16}) = v (\frac{0.08}{16.9728})

. Therefore,

v = \frac{10 \times 16.9728}{3 \times 0.08} = 707.2 m/s

. The answer is (D).

JEE Main · 2022 · 28 Jun 2022 · Shift 1 · Single correct option