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An ambulance siren has frequency 250 Hz. The ambulance is headed towards an accident site with a speed of 90 km /h. Two police officers on separate motor cycles head for the same accident site: one follows the ambulance with a speed of 80 km/h and the other approaches the accident site from the other direction with a speed of 80 km/h. What frequency does ambulance siren has for each of the police officers? Take the speed of sound equal to 340 m/s.

An ambulance siren has frequency 250 Hz. The ambulance is headed towards an
accident site with a speed of 90 km /h. Two police officers on separate motor
cycles head for the same accident site: one follows the ambulance with a speed of
80 km/h and the other approaches the accident site from the other direction with a
speed of 80 km/h. What frequency does ambulance siren has for each of the police
officers? Take the speed of sound equal to 340 m/s.

Grade:12th pass

1 Answers

Arun
25763 Points
3 years ago
We use the equation for the Doppler Effect: 𝑓=(𝑐+π‘£π‘Ÿ/(𝑐+𝑣𝑠))𝑓0
where c is the velocity of waves in the medium; vr is the velocity of the receiver relative to the medium; positive if the receiver is moving towards the source (and negative in the other direction); vs is the velocity of the source relative to the medium; positive if the source is moving away from the receiver (and negative in the other direction).
If the speeds vs and vr are small compared to the speed of the wave, the relationship between observed frequency f and emitted frequency f0 is approximately 𝑓=(1+Δ𝑣/𝑐)𝑓0
Police officer follows the ambulance 𝑓=(1+ (22.2 π‘š/π‘ βˆ’25 π‘š/𝑠)/ 340 π‘š/𝑠)Γ—250 𝐻𝑧=247.9 𝐻𝑧
Police officer moving towards the ambulance 𝑓=(1+(25 π‘š/π‘ βˆ’22.2 π‘š/𝑠)/ 340 π‘š/𝑠)Γ—250 𝐻𝑧=252 𝐻𝑧
Answer: πŸπŸ’πŸ•.πŸ— 𝑯𝒛 and πŸπŸ“πŸ 𝑯𝒛

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