As shown in the figure, a person is standing somewhere between two identical tuning forks that are each vibrating at 512 Hz . If both tuning forks travel towards the right at a speed of 5.5 m s ⁻¹ , determine the number of beats heard by the listener. The speed of sound in air is 330 m s ⁻¹ .

Step-by-step solution

Given: Frequency of tuning forks, f = 512 Hz Speed of tuning forks, v_s = 5.5 m s ⁻¹ Speed of sound, v = 330 m s ⁻¹ The tuning fork on the left moves towards the stationary listener. The apparent frequency heard by the listener is: f₁ = f ( v v - v_s ) The tuning fork on the right moves away from the stationary listener. The apparent frequency heard by the listener is: f₂ = f ( v v + v_s ) The number of beats heard by the listener is the difference between these two apparent frequencies: f_B = f₁ - f₂ = f ( v v - v