Question

1. a police car has a siren with a frequency of 400 Hz. when the car travels 20 m/s towards a building, the sound bounces off the building back towards the car. what beat frequency is heard in the car? Answer is 49.5 Hz please explain how

2. A charge of 8 nC is placed 2 meters to the west of the origin and a charge of -4 nC is placed 1 meter to the south of the origin. find the resulting magnitude of the electric field. Answer is 40 N/C please explain how.

Answer 1

Frequency of the sound heard in the car is given by actual frequency*[( speed of sound + speed of car towards the building )/ ( speed of sound - speed of car towards the building )] = 400*(343+20)/(343-20)= 449.5Hz

So the beat frequency heard in the car is= difference of both frequencies= 449.5-400= 49.5Hz

Field at the origin due to q1= 8 Nano coulomb is F1= k*q1/2^2 and is away from the charge towards the East

Where k=9*10^9

also field at the origin due to q2= - 4 Nano columbs is F2= kq2/1^2 and as directed away from the charger towards the north .

Now has both these fields are at perpendicular directions to each other, the resulting magnitude of the electric field is given by (F1^2+F2^2)^1/2 = 40N/C