Question

You hear sounds at the following decibel levels: 5 dB, 10 dB, 20 dB, and 40 dB. Which sound is 10 times higher than the lowest pressure humans can hear?

A. 5 dB

B. 10 dB

C. 20 dB

D. 40 dB

**Not sure how to find this!! :( Thank you!!:)

Answer 1

we have to use this definition:
\[\Large N = 10{\log _{10}}\left( {\frac{{{P_1}}}{{{P_0}}}} \right)\]
where N is the number of decibels, and P_0 is a reference pressure

Answer 2

oh okay! how can we find what to plug in?

Answer 3

we have to know how much is the lowest pressure

Answer 4

ohhh would the lowest pressure be the 5 dB?

Answer 5

oh oops

Answer 6

or wait, it is 5 dB? :/

Answer 7

no, sorry, we can answer to your problem without know how much is the lowest pressure. Since we can write the lowest pressure as our reference pressure, and we can set P_1 = 10*P_0

Answer 8

ohh okay! :)

Answer 9

so we have:
\[\Large \begin{gathered}
{P_1} = 10{P_0} \hfill \\
N = 10{\log _{10}}\left( {\frac{{10{P_0}}}{{{P_0}}}} \right) = ...? \hfill \\
\end{gathered} \]

Answer 10

10?

Answer 11

ok! 10 dB

Answer 12

ohh so that is our solution? 10 dB? :O

Answer 13

yes!

Answer 14

woo! thank you!!:D

Answer 15

thanks! :)