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The siren of a fire engine that is driving northward at 31.0 m/s emits a sound of frequency 2160 Hz. A truck in front of this fire engine is moving northward at 19.0 m/s.
A. What is the frequency of the siren's sound that the fire engine's driver hears reflected from the back of the truck (Hz)?
B. What wavelength would this driver measure for these reflected sound waves (m)?



Answer :

OneeRa

(a) The frequency of the siren's sound that the fire engine's driver hears reflected from the back of the truck is 2243.9Hz.

(b) The wavelength of the reflected sound waves by the listener is 0.143 m.

We use the principle of Doppler's effect to find the results.

What is the Doppler's effect?

The Doppler's effect is a phenomenon when the source of a wave and an observer move relative to each other, the frequency heard is not the same with the actual frequency.

The equation of the Doppler's effect is

f₀ = (v + v₀) fs / (v + vs)

Where

  • f₀ = observer frequency of sound
  • v = speed of sound waves (340 m/s)
  • v₀ = observer velocity
  • vs = source velocity
  • fs = actual frequency of sound waves

Note:

  • v₀ (-) if it moves away from the sound source.
  • vs (-) if it moves closer to the observer.

There are a truck and a fire engine emitting a siren sound moving in the same direction.

  • The actual frequency, fs = 2160 Hz.
  • The fire engine velocity (source), vs = 31.0 m/s.
  • The truck velocity (observer), v₀ = 19.0 m/s.

Determine the frequency and the wavelength of the sound waves heard by the listener in the front!

We have the truck is in front of the fire engine. So, the sound source moves closer and the observer moves away. Then, frequency of the sound waves heard by the observer is

f₀ = (v - v₀)/(v - vs) × fs

f₀ = (340 - 19.0)/(340 - 31) × 2160

f₀ = (321/309) × 2160

f₀ = 2243.9 Hz

The wavelength of the sound waves heard by the observer is

λ₀ = (v - v₀) / f₀

λ₀ = (340 - 19) / 2243.9

λ₀ = 321 / 2243.9

λ₀ = 0.1430545

λ₀ = 0.143 m

Hence,

(a) The observer frequency of sound is 2243.9Hz.

(b) The wavelength of the reflected sound waves by the observer is 0.143 m.

Learn more about Doppler's effect here:

brainly.com/question/12674116

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