Question

1.

The intensity level of the sound reaching your ear from a speaker 25 m away is 110 dB.

(a) What is the intensity?

(Answer: 0.10 W/m2)

(b) If you move to a new distance of 7.9 m, what is the new sound intensity level in

decibels?

(Answer: 120 dB)

(c) What is the power output of the speaker?

(Answer: 784 W)

Answer 1

Relation between Intensity and Intensity level is given by:

SL = 10*log (I/I0)

I0 = Threshold intensity for humans = 10^-12 W/m^2

SL = Intensity level = 110 dB

So,

110 = 10*log (I/I0)

log (I/I0) = 11

I/I0 = 10^11

I = I0*10^11 = 10^-12*10^11

I = 10^-1 = 1/10 = 0.10 W/m^2

Part B.

Now relation between Intensity and distance from source is given by:

I = P/A = I/(4*pi*R^2)

P = Power of source, It is constant since source is same

So Intensity is inversely proportional to the square of distance from source, So

I2/I1 = (R1/R2)^2

R1 = 25 m

R2 = 7.9 m

So,

I2 = I1*(R1/R2)^2

I2 = 0.10*(25/7.9)^2 = 1.00 W/m^2

Now for this intenisty, new sound intensity level will be

SL2 = 10*log (I2/I0)

SL2 = 10*log (1.00/10^-12)

SL2 = 10*log (10^12)

SL2 = 10*12*log 10

Since log 10 = 1, So

SL2 = 120 dB

Part C.

Intensity = P/A

Use any of the intensity and distance

P = I*A = I*4*pi*R^2

for R = 7.9 m, I = 1.00 W/m^2, So

P = 4*pi*7.9^2*1.00

P = 784 W

Please Upvote.