Chapter 8.7, Problem 73STP

Y13

To determine

To find: The difference of loudness between $1$ and $10$ alarm clocks.

Answer to Problem 73STP

The difference of $10$ alarm clock is louder $10$ decibels than $1$ alarm clock

Explanation of Solution

Given information:

The given sound of 1 alarm clock $\text{8}0\text{ decibels}.$

Calculation:

Formula:

  $L=10{\log }_{10}R$

Where,

  $L$ = loudness of sound

  $R$ = relative intensity

Consider the loudness level:

  $L=10{\log }_{10}R$

Here, $L=10{\log }_{10}R$ is the relative intensity.

Consider the intensity of one alarm clock of loudness level 80 decibels is $R$ .

Therefore, the loudness level of 10 alarm clock relative to one is:

  $\begin{array}{c}L=10{\log }_{10}\frac{10R}{R}\\ =10{\log }_{10}10\\ =10\end{array}$

Therefore, the difference of $10$ alarm clock is louder $10$ decibels than $1$ alarm clock.