Question

A person standing 1.25 m from a portable speaker hears its sound at an intensity of 7.90 ✕ 10⁻³ W/m².

HINT

(a)

Find the corresponding decibel level.

  dB

(b)

Find the sound intensity (in W/m²) at a distance of 36.0 m, assuming the sound propagates as a spherical wave.

  W/m²

(c)

Find the decibel level at a distance of 36.0 m.

Answer 1

Part A. Sound's decibel level is given by:

SL = 10*log (I/I0)

I = Intensity of sound produced by speajer at 1.25 m = 7.90*10^-3 W/m^2

I0 = Human threshold intensity = 10^-12 W/m^2

So,

SL = 10*log (7.90*10^-3/10^-12) = 98.97627 dB

SL = 99.0 dB

Part B.

Since power source is constant, So

Power = Intensity*Area

So,

I1*A1 = I2*A2

A = Surface area of spherical wave = 4*pi*R^2

I1*4*pi*R1^2 = I2*4*pi*R2^2

I2 = I1*(R1/R2)^2

I2 = 7.90*10^-3*(1.25/36.0)^2

I2 = 9.52*10^-6 W/m^2

Part C.

Now Sound decibel level at 36.0 m will be:

SL1 = 10*log (I1/I0)

SL1 = 10*log (9.52*10^-6/10^-12) = 69.786 dB

SL = 70.0 dB

Let me know if you've any query.