Question

A woman is sitting at a bus stop when an ambulance with a siren wailing at 317 Hz approaches at 69 miles per hour (mph). Assume the speed of sound to be 343 m/s. a) How fast is the ambulance moving in meters per second? (perform the necessary unit conversion) Vs= 69 mph = m/s b) What frequency does the woman hear? fa = Hz c) What speed (vs) would the ambulance be traveling in order for the woman to hear the siren at an approaching frequency of 350 Hz? Vs= m/s d) What frequency would she hear as the siren moves away from her at the same speed (as in part c)? fa = Hz

Answer 1

a) 30.84m/s

b) 348.32Hz

c) 32.34m/s

d) 289.69Hz

Step-by-step explanation:

a) If 1 mile=1609,34m, and 1 hour=3600 seconds, then 69mph=69*1609.34m/3600s=30.84m/s

b) Based on Doppler effect:

/*I will take as positive direction the vector
`\vec r_(observer)-\vec r_(emiter)` */

`f_(observed)=((v_(sound)-v_(observed))/(v_(sound)-v_(emited)))f_(emited)`

`f_(observed)=((343m/s-0m/s)/(343m/s-30.84m/s))317Hz=348.32Hz`

c)
`350Hz=((343m/s-0m/s)/(343m/s-v_(ambulance)))317Hz, V_(ambulance)=343m/s-(317Hz)/(350Hz).343m/s=32.34m/s`

d)
`f_(observed)=((343m/s-0m/s)/(343m/s+32.34m/s))317Hz=289.69Hz`