Question

A 45 dB sound wave strikes an eardrum whose area is 4.1

Answer 1

a) sound intesity level, beta = 10*log*(I/Io)

here, Io = 10^-12 W/m^2

45 = 10*log(I/10^-12)

4.5 = log(I/10^-12)

==> I = 10^4.5 * 10^-12

= 3.16*10^-8 W/m^2


Power = Intenisty*area

= 3.16*10^-8*4.1*10^-5

= 1.297*10^-12 W

b) Energy = power*time

time = energy/power

= 1/1.297*10^-12

= 7.71*10^11 s

= 7.71*10^11/(365*24*60*60)

= 24448.2 years

Answer 2

A 48 dB sound wave strikes an eardrum whose area is 4.9 10-5 m2

Given:

Area=4.9 x 10^-5 m2
48db= Intensity in db

Convert intensity in decibels to intensity in watts/m2:

48db=10 log (I / 1 x 10^-12)

divide both sides by 10.
48db/10=10 log ( I/ 1x 10^-12)/10

4.8db=log (I/1 x 10^-12)

use the law on logarithms.(b^y=x)

In this case, 4.8 is our y, 10 is our base and (I/ 1x 10^-12) is our x.

(Remember that every logarithmic equation, if it has no specific base, has a base of 10.)

10^4.8=I / 1 x10^-12

(eliminate the log expression)

6.30957344 x 10^4=I / 1 x 10^-12

cross multiplying we get,

6.30957344 x 10^-8 watts/m2= Intensity in watts/m2.

we round off this value to 6.31 x 10^-8 watts/m2.

we use this intensity for calculating power.

I=P/A
6.31X10^-8watts/m2= P/ 4.9 x 10^-5 m2

cross multiplying, we get:

3.09 x 10^-12 watts.

calculating for the energy,
t= 1s
Break down watts into J/s
3.09 x 10^-12 J/s= E / 1S
3.09x10^-12 J = energy absorbed per second.

Solving for time,

P= E / T
3.09 x 10^-12 J/s = 1.0 J/ T

cross multiplying, we get:

3.09 x 10^-12 J (T)=(1.0J)(s)

then divide 3.09 x 10^-12 J by itself to isolate the unknown. Do the same thing on the other side of the Eq.

T= 1.0J(s)/(3.09 x 10^-12J)

You get:

T= 3.24 x 10^11 s

I hope it helped you!!!

Answer 3

a> 45 = 10 log ( I/10^-12)

=> I = 3.16*10^-8

energy =3.16*10^-8 * 4.1*10^-5=1.29*10^-12

b> time =1/1.29*10^-12 =7.7*10^11 sec

Answer 4

Db = 10 log (I/I0)

at 45db

4.5 = log I/I0

I/I0 = 10^4.5

I = 10^4.5 *10^-12

I = 3.16*10^-8

Power = I*area

P = 1.296 *10^-12 J/s

this energy in 1sec,

1.296 *10^-12 J in 1 sec

so 1J will be in 7.71 *10^11 sec