A fire truck is parked 1 50 meters from an observer, the air temperature is 35 d

Question

A fire truck is parked 1 50 meters from an observer, the air temperature is 35 degree C. The siren is initially off. When the siren is turned on, how long does it take the sound to reach the observer? The siren's loudness at the observer's position is beta = 75 dB. What is the intensity I of the sound, in W/m^2? What is the power P emitted by the siren? The observer moves away from the truck until the loudness decreases to 65 dB. How far did the observer move from her original position? The siren's sound waves have a wavelength lambda = 1.5 m. Calculate the source frequency f_s of the sound waves. The truck moves away from the observer at velocity u_s = 45 mi/hr. At the same time, the observer moves away from the truck at velocity u_o = 12 mi/hr. What frequency f_o is heard by the observer?

Explanation / Answer

a) speed of sound v =343.3 m/s

t= d/v = 150/ 343.3 = 0.44 sec

b) loudness = 10 log ( I / I0)

75 = 10 log(I / 10^-12)

I / 10^-12 = 10^7.5

I = 3.16 x 10^-5 W / m^2 ..........>>Ans

I = P / 4pir^2

P = (3.16 x 10^-5)( 4x pi x 150^2) = 8.94 W

c) for 65 dB ,

65 = 10 log(I / 10^-12)

I = 3.16 x 10^-6 W/m^2

P = I * 4pir^2

8.94 = 3.16 x 10^-6 x 4 x pi x r^2

r = 474.31 m

distance moved = 474.31 - 150 = 324.31 m

d) frequency = speed / wavelength

    fs = 343.3 / 1.5 = 228.87 Hz

e) us =45 x 1609m / 3600sec = 20.11 m/s

u0 = 12 x 1609 / 3600 = 5.36 m/s

using doppler effect,

f = ( v - u0)fs / (v - vs)

f = (343.3 - 5.36)*228.87 / (343.3 - 20.11)

f = 239.32 Hz

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