Question

You are located 35 meters away from a large blasting speaker at a concert. It is very loud from where you are, registering a reading of 82 on a decibel meter that you just happen to have casually.

A) what is the power output of the speakers in watts?

B) how close would you have to be in order for the music to have a reading of 120 dB? how far away would someone have to be in order for the sound to be inauduble (0 dB)?

C) how long does it take the sound from the speakers to reach you? the temperature is 59? F.

D) explain why the sound would be even louder if you were in an indoor venue.

Answer 1

a)

db = decibal reading = 82 dB

r = distance = 35 m

I = intensity = ?

Using the equation

db = 10 log₁₀(I/I_o)

82 = 10 log₁₀(I/10^-12)

I = 1.6 x 10^-4 W/m²

power is given as

P = I (4r²)

P = (1.6 x 10^-4) (4 x 3.14) (35)²

P = 2.5 Watt

b)

db = decibal reading = 120 dB

I = intensity = ?

Using the equation

db = 10 log₁₀(I/I_o)

120 = 10 log₁₀(I/10^-12)

I = 1 W/m²

power is given as

P = I (4r²)

2.5 = (1) (4 x 3.14) r²

r = 0.45 m

db = decibal reading = 0 dB

I = intensity = ?

Using the equation

db = 10 log₁₀(I/I_o)

0 = 10 log₁₀(I/10^-12)

I = 10^-12 W/m²

power is given as

P = I (4r²)

2.5 = (10^-12) (4 x 3.14) r²

r = 4.5 x 10⁵ m