Register to reply

How to calculate sound intensity when given decibels

Tags: decibels, intensity, sound
Share this thread:
Jan13-09, 08:03 PM
P: 100
1. The problem statement, all variables and given/known data

When a person wears a hearing aid, the sound intensity level increases by 30.0 dB. By what factor does the sound intensity increase?

2. Relevant equations

B = (10 dB) log (Ia/Ib)

Ia = sound intensity
Ib = threshold of human hearing (1.0 * 10^-12 W/m^2)

3. The attempt at a solution

I used the equation above, substituting into it:

30 dB = (10 dB) log (Ia/1.0 * 10^-12 W/m^2)

I divided both sides by 10 dB to get rid of the 10 dB on the right side of the equation.

3 = log (Ia/1.0 * 10^-12 W/m^2)

Then I converted this into regular exponential form without logs:

10^3 = (I/1.0 * 10^-12 W/m^2)

I get 1.0 * 10^-9 for I, but my answer key says the answer is 1000. This is 10^3, which I seem to have, but I still have an unknown - I - in the equation.

Phys.Org News Partner Science news on
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history
Jan13-09, 09:07 PM
HW Helper
P: 3,394
Your answer of I = 1.0 * 10^-9 is correct.
But the question doesn't ask for I, it asks by what factor has I increased - presumably from 0 db which is the threshold of hearing. So divide your answer for I by the value of Ib.
Jan13-09, 09:08 PM
HW Helper
P: 6,204
Quote Quote by DMOC View Post

10^3 = (I/1.0 * 10^-12 W/m^2)
Right there is your answer. The wanted the factor, I/I0, not the intensity to give 30dB

Jan13-09, 09:32 PM
P: 100
How to calculate sound intensity when given decibels

So I got the right answer all was just that I had to realize that the question asked for what (Ia/Ib) was equal to, not just Ia.


Register to reply

Related Discussions
Decibels and intensity Introductory Physics Homework 1
Decibels and intensity Introductory Physics Homework 4
Sound Wave Intensity/Sound Level Introductory Physics Homework 1
Sound Intensity and Sound Waves Introductory Physics Homework 5
The sound of Decibels General Physics 7