Question

A fire truck with sirens on, is driving north on a street. A car is driving south on the same street and sees the fire truck ahead. The car is moving at a speed of 15.7 m/s and the fire truck is moving at a speed of 31.8 m/s. The siren of the fire truck produces a 965 Hz sound. The speed of sound in air is 343 m/s. What frequency does the person in the car hear? If the sound from the siren is produced at 45.2 W, what is the reading on the decibel meter held by the person when the car is 36.8 m away from the fire truck? Assume the sound from the horn is emitted uniformly in all directions (A = 4 pi r^2). What is the farthest distance from the fire truck that a person could hear the siren?

Answer 1

Part a)

f = 1112.3 Hz

Part b)

L = 94.2 dB

Step-by-step explanation:

Part a)

As we know by Doppler's Effect of sound that when source of sound and observer moves relative to each other then the frequency of sound observed by the observer is different from actual frequency

Here when source and observer is moving towards each other then the observed frequency is given by

`f = f_o(v + v_0)/(v- v_s)`

now plug in all values in it

`f = 965 ((343 + 15.7)/(343 - 31.8))`

`f = 1112.3 Hz`

Part b)

Power of the siren is given as

`P = 45.2 W`

Now the intensity of sound received by driver of car is given as

`I = (P)/(4\pi r^2)`

`I = (45.2)/(4\pi (36.8)^2)`

`I = 2.66 * 10^(-3) W/m^2`

now the decibel level of sound is determined by

`L = 10 Log (I)/(I_o)`

now we have

`L = 10 Log(2.66 * 10^(-3))/(10^(-12))`

`L = 94.2 dB`