Two identical tuning forks, each of frequency 1700 Hz, move along the same line relative to a stationary observer. One approaches and the other recedes with the same small speed u, where u is much smaller than 340 m/s. The observer hears 20 beats per second. If u = N m/s, find N.
Physics · Wave Motion · doppler effect
JEE Mains NEET JEE Advanced

Question

Two identical tuning forks, each of frequency 1700 Hz, move along the same line relative to a stationary observer. One approaches and the other recedes with the same small speed u, where u is much smaller than 340 m/s. The observer hears 20 beats per second. If u = N m/s, find N.

Physics · Wave Motion · doppler effect

G1 Physics · Accepted Answer

For a small source speed, fₐ ≈ f×(1+u/v), fᵣ ≈ f×(1−u/v). Therefore the beat frequency is approximately fᵦ ≈ 2f×u/v. Substitute fᵦ = 20 Hz, f = 1700 Hz, v = 340 m/s. Thus, 20 = 2×1700×u/340 = 10u. Hence, u = 2 m/s. Therefore, N = 2.