# Question on sound intensity and dB

Krystal111
Homework Statement:
By what factor is the sound intensity reduced if ear protectors can reduce sound levels by 40dB?
Relevant Equations:
I can't seem to find any
Would we have to use the 3-dB exchange rate? How would we solve this question?

Homework Helper
Gold Member
2022 Award
Homework Statement:: By what factor is the sound intensity reduced if ear protectors can reduce sound levels by 40dB?
Relevant Equations:: I can't seem to find any

Would we have to use the 3-dB exchange rate? How would we solve this question?

Krystal111
A decibel would be a unit of measurement that is equal to one tenth of a bel.

Arjan82

Krystal111
It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a power ratio of 101/10 or root-power ratio of 10¹⁄²⁰ - as per what wikipedia states

Mentor

@Krystal111 first, all caps in a thread title is the Internet equivalent of shouting. Second, the title of your thread should be a brief description of your question, not a statement (irrelevant to anyone responding here in any case) that you need help, let alone need help "ASAP". Please review the rules for posting homework questions.

Arjan82
Great, so you can cite Wikipedia. Now what does this all mean? It literally tells you the power ratio for 1 dB, so how would you translate that to 40dB? And what is intensity? How is that related to power?

Arjan82
And... what in the world does the 3-dB exchange rate have to do with anything? Do you know what that is?

Homework Helper
Gold Member
2022 Award
It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a power ratio of ##10^{1/10 }## or root-power ratio of 10¹⁄²⁰ - as per what wikipedia states
Right. But can you convert that to an equation that gives the sound intensity ratio in terms of the dB difference?
Or you could cheat and scroll down the Wikipedia entry to find a table expressing 40dB as a power ratio and as an amplitude ratio. Then you just have to pick which of those is the same as sound intensity.