Two identical tuning forks vibrating at a common frequency of 256 Hz are held stationary at some distance apart. A listener runs between the tuning forks at a speed of 3.0 m/s , approaching one tuning fork while receding from the other, as shown in the figure. Determine the beat frequency observed by the listener. Assume the speed of sound in air to be 332 m/s .

Step-by-step solution

The apparent frequency heard by the listener from the tuning fork being approached is given by Doppler's effect: f₁ = f ( v + v_L v ) The apparent frequency heard from the tuning fork being receded from is: f₂ = f ( v - v_L v ) The beat frequency observed by the listener is the difference between these two frequencies: f_b = f₁ - f₂ = f ( v + v_L v ) - f ( v - v_L v ) f_b = f ( 2v_L v ) Substituting the given values ( f = 256 Hz , v_L = 3.0 m/s , v = 332 m/s ): f_b = 256 ( 2 3.0 332 ) f_b = 1536 332 4.6 Hz