Acar is stopped at a traffic light. when the light turns green, the car starts from rest with an acceleration of 2.5 m/s2 . also, as the light turns green, a truck traveling with a constant velocity of 10 m/s passes the car. the truck’s horn is stuck, emitting sound at a frequency of 440hz. what frequency of sound is heard by the driver of the car, (a) 5 seconds before the light turned green? (b) 5 seconds after the light turned green? (c) 10 seconds after the light turned green?

Doppler effect is used to find the change in wave frequency when either the observer or source or both are moving

(a) 5 seconds before the light turned green, the frequency of sound heard by the observer is 453. Hz

(b) 5 seconds after the light turned green the frequency of the sound heard by the observer is approximately 443.12 Hz

(c) 10 seconds after the light turned green the frequency heard by the light is 420. Hz

The reason the above values are correct is given as follows;

The given parameters are;

Initial velocity of the car = 0 (Starts from rest)

Acceleration of the car, a = 2.5 m/s²

The constant velocity of the truck that passes the car, = 10 m/s

Frequency of the sound emitted by the truck, f = 440 Hz

(a) The frequency of the sound heard by the driver of the car 5 seconds before the light turns green is given as follows;

The Doppler shift formula is given as follows;

Where;

v = The speed of sound in air ≈ 343 m/s

Therefore;

The frequency of sound heard by the observer, f' = 453. Hz

(b) The speed of the car t = 5 seconds after the light turns green is given as follows;

v = u + a·t

∴ v = 0 + 2.5 × 5 = 12.5

The speed of the car, 5 seconds after the light turns green, = 12.5 m/s

The position of the car at 5 seconds after the light turns green is given as follows;

u = 0

The position of the truck after 5 seconds = 5 s × 10 m/s = 50 m

Therefore, the car is moving towards the truck, which is moving away from the car

The correct formula to use is therefore;

The frequency of the sound heard by the driver, f' ≈ 443.12 Hz

(c) 10 seconds after the light turns green, we have;

v = 0 + 2.5 × 10 = 25

The velocity of the car = 25 m/s

The position of the car, s₁₀, is given as follows;

The position of the car, s₁₀ = 125 m

The position of the truck, d₁₀ = 10 s × 10 m/s = 100 m

Therefore, the car is ahead of the truck, and the equation to be used is therefore;

Which gives;

The frequency of the sound heard by the driver, f' = 420. Hz

Learn more about the Doppler effect here:

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