Question

You stand 30 m from a large speaker at a concert, and the intensity of the sound you hear from that speaker is 4×10⁻² W/m2 .

How much power is the speaker emitting?

What is the intensity of the sound from the speaker at a distance of 60 m ?

The pain threshold for humans is a sound intensity level of about 120dB. At what distance from this speaker would the sound be painful?

Answer 1

Here,

for the power emitted

Power emitted = Intensity/Area

Power emitted = 4 *10^-2 * 4pi * 30^2

Power emitted = 452 W

Power emitted is 452 W

for the intensity of the sound at 60 m

Intensity at 60 m = Power/(4pi * r^2)

Intensity at 60 m = 452/(4pi * 60^2)

Intensity at 60 m = 0.01 W/m^2

the intensity at 60 m is 0.01 W/m^2

for let the distance is x

for the sound level

120 = 10 * log(I/(1 *10^-12))

I = 1 W/m^2

for the distance

1 = 452/(4pi * d^2)

d = 6 m

the least distance is 6 m