Question

You are walking towards your friend swinging a buzzer at the end of a rope. The buzzer swings in a circle with a radius of 1.000 m. Sometimes the buzzer is moving at your friend and sometimes it is moving away. It takes 0.5000 s for the buzzer make one rotation. Your friend hears a high frequency of 160.0 Hz and a low frequency of 148.5 Hz. If the speed of sound is 340 m/s, how fast are you walking?

Please provide as much steps and details for the answer to help me understand the question

Answer 1

For buzzer moving towards friend

velocity of buzzer = 2 * 3.14 * 1/0.5 = 12.56   m/sec

=>   According to Doppler effect

=>    160 = f * [340/(340 - v - 12.56)]             -------------> 1)

For buzzer moving away from friend

=> 148.5 =   f * [340/(340 - v + 12.56)]             ---------------> 2)

From 1) and 2)

=> 160/148.5 =   (340 - v + 12.56)/(340 - v - 12.56)

=>   v = 2.92 m/sec           ---------------->   speed of walking