Question

The loudness of a sound in decibels is related to the intensity of the sound i, where the function for the loudness is given by L(i)=101og10(i/i0), and io is a constant equal to the minimum sound that can be detected by the human ear.
a. Find the loudness in decibels of a rock music recording with an intensity of 10 million times io.

Answer 1

\[L(i)=10\log_{10}(\frac{i}{i_0})\]and you are told to find loudness of music that has:\[i=10,000,000*i_0=10^7*i_0\]so you get:\[L(i)=10\log_{10}(\frac{10^7*i_0}{i_0})\]the \(i_0\)'s cancel and you should then be able to calculate the loudness.

Answer 2

So it would come out to be L(i)=10log10(10^7)?

Answer 3

Then I calculate?

Answer 4

yes, and you should be able to simplify the log

Answer 5

\[\log_{10}(10^a)=a\]

Answer 6

therefore:\[\log_{10}(10^7)=?\]

Answer 7

7? http://www.wolframalpha.com/input/?i=log10%2810%5E7%29

Answer 8

yes 7, but you didn't need wolfram for that, I showed you the rule above ^^^

Answer 9

so now you should be able to calculate the value for loudness

Answer 10

Oh woops :/ Yea, thank you! a refers to the 7.

Answer 11

yes :)

Answer 12

So would the answer be 7 million?

Answer 13

no....

Answer 14

\[L(i)=10\log_{10}(\frac{10^7*i_0}{i_0})=10\log_{10}(10^7)=10*7=?\]

Answer 15

I meant 70 million. But nvm. 10*7=70

Answer 16

yes, answer is 70 (not 70 million)

Answer 17

Oh o.k. Thank you so much for your help asnaseer!

Answer 18

yw - I'm glad I was able to help :)

Answer 19

Would you happen to understand this question? c.In terms of decibels, how close is the intensity level of the rock music recording to the threshold of pain?

Answer 20

I think you'll need to google that. try and search for how many decibels a human ear can stand before it becomes painful.
for rock music I guess the loudness is 70 decibels from the equation above.

Answer 21

O.k cool. Thanks!

Answer 22

IIRC the threshold of pain for the human ear is 120dB, but you might wanna check that