Question

117.7P120. The frequency of the siren of an ambulance of the ambulance (in mph) if the speed of sound is v 345.00 m/s? is 920 Hz and is approaching you. You are standing on a corner and observe a frequency of 985 Hz. What is the speed mph

Answer 1

Given that,

Observer frequency (Fo)= 985 Hz

Siren frequency (Fs)= 920 Hz

Speed of a sound (v) =345 m/s

let,

Vo is the observer velocity =0 m/s

and Vs is the velocity of ambulance.

then

Fo = Fs {[V+Vo]/[V-Vs]}

substitute all the values in above equation,

we get,

985 Hz = 920 Hz {[345 m/s+0 m/s]/[345 m/s - Vs]}

985 Hz =920 Hz {345 m/s/[345 m/s -Vs ]}

985 HZ/920 Hz ={345 m/s/[345 m/s -Vs]}

1.0706 ={345 m/s/[345 m/s -Vs ]}

{345 m/s/[345 m/s -Vs ]} =1.0706

345 m/s =1.0706 *[345 m/s -Vs ]

345 m/s =369.375 m/s -1.0706 Vs

1.0706 Vs =369.375 m/s -345 m/s

1.0706 Vs = 24.375 m/s

Vs = 24.375 m/s/1.0706

Vs=22.7676 m/s

Vs=22.7676 m/s *3600

Vs=81963.36 mph.