A siren emitting a sound of frequency 2000 Hz moves away from you towards a cliff at a speed of 8 m/s.
(a) What is the frequency of the sound you hear coming directly from the siren.
(b) What is the frequency of sound you hear reflected off the cliff. Speed of sound in air is `330(m)/(s)`.

Explanation

(a) The frequency of sound heard directly.
`f_1=f_0((v)/(v+v_S))`
`v_S=8(m)/(s)`
`f_1=((330)/(330+8))xx2000`
`f_1=(330)/(338)xx2000=1953Hz`
(b) the frequency of the reflected sound is given by
`f_2=f_0((v)/(v-v_S))`
`f_2=((330)/(330-8))xx2000`
`f_2=(330)/(322)xx2000=2050Hz`