Question

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?

Answer 1

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:

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