A small source of sound vibrating at a frequency of 500 Hz is rotated in a circle of radius 100/ cm with a constant angular speed of 5.0 revolutions per second. A listener is situated in the plane of the circle. Determine the minimum and maximum frequencies of the sound observed. The speed of sound in air is 332 m s ⁻¹ .

Step-by-step solution

The linear speed of the source is given by v_s = R . Given the radius R = 100 cm = 1 m and angular speed = 5.0 rev/s = 10 rad/s , we get: v_s = ( 1 )(10 ) = 10 m/s The maximum frequency is observed when the source moves directly towards the listener: f_ max = f₀ ( v v - v_s ) = 500 ( 332 332 - 10 ) = 500 ( 332 322 ) 515.5 Hz The minimum frequency is observed when the source moves directly away from the listener: f_ min = f₀ ( v v + v_s ) = 500 ( 332 332 + 10 ) = 500 ( 332 342 ) 485.4 Hz The closest values are 485 H