Question

An 8-hour exposure to a sound intensity level of 90.0 dB may cause hearing damage. What energy in joules falls on a 0.800-cm-diameter eardrum so exposed?

Answer 1

Answer:

1.44x10⁻³J

Explanation:

Given :

Time = 8hrs *(3600secs/1hr)= 28.8*10³seconds

Intensity= 90dB

D= 0.008m

Radius=0.008m/2

=0.004m

the sound level in decibel can be expressed below as

I=10dBlog[I/I₀]

where I₀=10⁻¹²/m² which is the refrence intensity

90=10log[I/10⁻¹²]

I=0.001W/m²

we know that intensity of the wave which id the average rate per unit area which energy is transfered can be calculated using below formular

I = P/A

where P= powerr which is renergy transfer at a time

A= area= πr²

making P subject of formular we have

P= I πr²

= 5.02 x10⁻⁸W

Energy =power x time

E=28800*5*10⁻⁸

=0.001443J

therefore,the energy in joules is 1.44x10⁻³J

Answer 2

Answer:

1.4E-3J

Explanation:

Given that

Time = 8hrs = 28.8E3 seconds

Intensity= 90dB

D= 0.008m

Radius= 0.004m

So intensity is sound level Bis

10dBlog(I/Io)

I= 10 (B/10dB)Io

= 10( 90/10) x 10^-12

=0.001W/m²

But we know that

I = P/A

P= I πr²

= 5.02 x10^-8W

But energy is power x time

So E= 5.02E-8 x 28.8E3

= 1.4E-3J