A car is stopped at a traffic light


Asked by maham237 @ in Physics viewed by 275 People


A car 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?

Answered by maham237 @



Answer:

a) f = 453.3Hz

b) f = 443.1Hz

c) f = 420Hz

Explanation:

First of all we need to know the positions and velocities of both vehicles.

For the car:

Xc(-5) = 0m; Vc(-5) = 0m/s

Xc(5) = 2.5*5^2/2=31.25m; Vc(5)=2.5*5 = 12.5m/s

Xc(10)=2.5*10^2/2=125m; Vc(10)=2.5*10=25m/s

For the truck:

Xt(-5)=10*(-5) = -50m; Vt(5)=10m/s

Xt(5)=10*5 = 50m; Vt(5)=10m/s

Xt(10)=10*10=100m; Vt(10)=10m/s

Now for part a) t=-5s. The truck is behind the car, so:

f=\frac{C}{C-Vt}*fo = 453.3Hz

Now for part b) t=5s. The car is behind the truck, so:

f=\frac{C+Vc}{C+Vt}*fo = 443.1Hz

Now for part b) t=10s. The truck is behind the car, so:

f=\frac{C-Vc}{C-Vt}*fo = 420Hz


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