A source of sound vibrating at frequency 500 Hz is rotated in a circle of radius 100 cm at a constant angular speed of 5 revolutions per second. A listener is in the plane of the circle. The maximum and minimum frequency of sound heard are Speed of sound on air = 332 m/s

Step-by-step solution

Given frequency of the source, f₀ = 500 Hz Radius of the circular path, R = 100 cm = 1 m Angular speed, = 5 rev/s = 5 2 rad/s = 10 rad/s Linear speed of the source, v_s = R = ( 1 )(10 ) = 10 m/s The maximum frequency is heard when the source moves directly towards the listener: f_ max = f₀ ( v v - v_s ) f_ max = 500 ( 332 332 - 10 ) = 500 ( 332 322 ) 515.5 Hz 516 Hz The minimum frequency is heard when the source moves directly away from the listener: f_ min = f₀ ( v v + v_s ) f_ min = 500 ( 332 332 + 10 ) = 500 ( 3