i.At a distance of 2.9 m from a point source of sound, the intensity level is 78

Question

i.At a distance of 2.9 m from a point source of sound, the intensity level is 78 dB. What will be the intensity level at a distance of 4 m from this source? The lowest detectable intensity is 1.0 × 10-12 W/m2. (Give answer to the nearest dB)

j.As you stand by the side of the road, a car approaches you at a constant speed, sounding its horn, and you hear a frequency of 84 Hz. After the car goes by, you hear a frequency of 62 Hz. What is the speed of the car? The speed of sound in the air is 343 m/s. (Give speed to the nearest m/s).

Explanation / Answer

We know that:

I = I0*10^(SL/10)

I1 = 10^-12*10^(78/10)

I1 = 6.309*10^-5 W/m^2

Since the power source is same,

Power = Intensity*Area

I1*A1 = I2*A2

I2 = I1*(A1/A2)

Area = 4*pi*R^2

I2 = 6.309*10^-5*(2.9^2/4^2)

I2 = 3.316*10^-5 W/m^2

Now

I2 = I0*10^(SL/10)

SL = 10*log (I2/I0)

SL = 10*log (3.316*10^-5/10^-12) = 75.21 dB

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