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$\cdot$ Find the intensity $\left($ in $W / m^{2}\right)$ of (a) a 55.0 dB sound, (b) a92.0 dB sound, (c) a $-2.0$ dB sound.

a) $3.16 \times 10^{-7} \mathrm{W} / \mathrm{m}^{2}$b) $1.58 \times 10^{-3} \mathrm{W} / \mathrm{m}^{2}$c) $6.31 \times 10^{-13} \mathrm{W} / \mathrm{m}^{2}$

Physics 101 Mechanics

Chapter 12

Mechanical Waves and Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

Rutgers, The State University of New Jersey

University of Winnipeg

McMaster University

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So let's find the intensity. We know that beta equals beta is the sound in decimal and decibels. So beta equals 10 log of thie intensity divided by the original, the initial intensity. So we can say that the initial intensity is going to be 10 to the 12th watts per meter squared, and we know that X equals log of Why? So we can say that Why equals tend to the ex. Now for a party. We know that beta equals 55. Is it 0.0 decibels? So we can say 5.5 zero equals log of eye over I not ah, which means that I equals eye not times 10 to the 5.5 power. And so we can say that the intensity is equal to 10 to the 5.5 power times 10 to the negative 12th and this is giving us 3.16 times 10 to the negative seventh watts per meter squared for part B beta equals 92.0 decibels. So we can say that I was going to be equal to 10 to the 9.2 power times, 10 to the negative 12 power again we just We're just using the same exact relationship. So the intensity is simply going to be equal to tend to the beta power times, the ah, I not to the initial intensity. So we can say that this is going to be equal to 1.58 times 10 to the negative third and for the last for part? See, we can do the entire thing. Once again, Beta is going to equal negative 2.0 decibels. So we can say that negative 0.20 is going to be equal to log of the intensity over the intensity. Not And so I was simply going to be able to the intensity, not times 10 to the negative 100.20 power S O. I was going to be equal to turn to the negative 12 times 10 to the negative 100.2. And this is going to be equal to 6.31 times 10 to the negative 13th watts per meter squared. And this will be our final answer. That is the end of the solution. Thank you for watching

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