Question

The velocity of sound in a gas, in which
superposition of two sound waves having
wavelengths 160 cm and 164 cm produces 20 beats
in 4 s, is
(1) 1312 m/s
(2) 300 m/s
(3) 364 m/s
(4) 328 m/s​

Answer 1

The velocity of sound in a gas is 328m/s . i.e Option (4) is correct

Explanation:

Given λ₁ =  160cm 1.60m and λ₂ = 164cm = 1.64m

Beat produce 20beats in 4 sec i.e 5beats per second

Velocity of sound = v = ?

We have  v = nλ then n = v/λ

Now n∝ 1/λ given λ₂>λ₁ Hence n₁>n₂

n₁-n₂ = 5

Therefore (v/λ₁ - v/λ2) = 5

v(1/λ₁- 1/λ₂) = 5

then solve this we get V = 328m/s