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 :

Solution

Physics sir · 4 steps

Same gas, same speed: write each frequency as v/λ and subtract to get the beats.

1. Beat frequency. 40 beats in 12 s means f_b = 40/12 = 10/3 Hz.
2. Two frequencies. Both waves travel through the same gas at the same speed v. So f₁ = v/4.08 and f₂ = v/4.16. The shorter wavelength has the higher frequency.

   v/4.08-v/4.16 = v (4.16-4.08)/(4.08 × 4.16) = 10/3

3. Solve for v. 4.08 × 4.16 = 16.9728, so v × 0.08/16.9728 = 10/3. This gives v = (10 × 16.9728)/(3 × 0.08) = 169.728/0.24 = 707.2 m s⁻¹.
4. So. The speed of sound in the gas is 707.2 m s⁻¹, which is option (d).

The idea to keep. When a beat question gives wavelengths, convert each one to a frequency with f = v/λ. Beats per second = f₁ - f₂, never half of it.

Answer from the NTA final answer key. Solution by PrepWiser.