A) A siren has a frequency of 650 Hz when it is at rest, whereas it has an appar

Question

A) A siren has a frequency of 650 Hz when it is at rest, whereas it has an apparent frequency of 771 Hz when it is moving toward a stationary observer. What is the speed of the siren in the latter case? ______m/s

B) A siren is approaching you at 48 m/s and is perceived to have a frequency of 1190 Hz. If the siren stops moving, what frequency do you now hear? _______Hz

C) The siren in an ambulance has a frequency (according to you) of 1095 Hz as it moves toward you at speed v. It then makes a U-turn and travels away from you with speed v, and you hear a frequency of 920 Hz. What is the final speed v of the siren? _______ m/s

Explanation / Answer

A) by dopplers formula,

f' = f v/(v-vs)

771 = 650*340/(340-v)

340-v = 650*340/771 = 286.64

v = 340-286.64

= 53.36 m/s

B) again, 1190 = f*340/(340-48)

f = 1190*292/340 = 1022 Hz

c) 1095 = f*340/(340-v)

920 = f*340/(340+v)

dividing the equations,

1095/920 = (340+v)/(340-v)

1095*340-1095v = 920*340+920v

v = 340*(1095-920)/(1095+920)

= 29.53 m/s

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