Question

Standing at a crosswalk, you hear a frequency of 510 Hz from the siren of an approaching ambulance. After the ambulance passes, the observed frequency of the siren is 427 Hz. Determine the ambulance's speed from these observations. (Take the speed of sound to be 343 m/s.)

Answer 1

ambulance speed is 30.38 m/s

Step-by-step explanation:

given data

hear frequency = 510 Hz

pass frequency = 427 Hz

speed of sound = 343 m/s

to find out

ambulance speed

solution

we consider here ambulance speed is v

so when we hear frequency velocity equation will be

510 = 343f / ( 343 - v ) ...........................1

and when ambulance pass velocity equation will be

427 = 343f / ( 343 + v ) ...........................2

so from equation 1 and equation 2

`(343f / ( 343 + v ) )/(343f / ( 343 - v ))` = 510 / 427

`(( 343 + v ))/(( 343 - v ))` = 510 / 427

solve it we get

v = 30.38 m/s

so ambulance speed is 30.38 m/s