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The sound level 9.00 $\mathrm{m}$ from a loudspeaker, placed in the open, is 115 $\mathrm{dB}$ . What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?

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Physics 101 Mechanics

Chapter 16

Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

University of Michigan - Ann Arbor

University of Washington

Simon Fraser University

University of Winnipeg

Lectures

08:15

In physics, sound is a vibration that typically propagates as an audible wave of pressure, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the reception of such waves and their perception by the brain. Humans can only hear sound waves as distinct pitches when the frequency lies between about 20 Hz and 20 kHz. Sound above 20 kHz is known as ultrasound and has different physical properties from sound below 20 kHz. Sound waves below 20 Hz are called infrasound. Different species have different hearing ranges. In terms of frequency, the range of ultrasound, infrasound and other upper limits is called the ultrasound.

04:49

In physics, a traveling wave is a wave that propogates without a constant shape, but rather one that changes shape as it moves. In other words, its shape changes as a function of time.

01:26

The sound level 12.0 $\mat…

06:16

The sound level 8.25 m fro…

01:22

01:38

A rock band (with loud spe…

02:27

A loudspeaker at a rock co…

00:36

A stereo speaker represent…

01:57

Suppose the sound intensit…

05:19

At a rock concert, a dB me…

05:56

(II) At a rock concert, a …

02:47

A stereo amplifier is rate…

04:05

At a painfully loud concer…

03:57

01:45

03:05

Assume a 150-W loudspeaker…

Assume a loudspeaker broad…

04:26

(II) At a painfully loud c…

decibels. What is the acoustic power output in Watts of the speaker? Assuming it radiates equally in all directions. I wrote them were given here or even that the, uh the power or I'm sorry, the decibel output beta is 150 best 115 decibels, right? We're also told that the, uh, distance away, which I write is our is nine. And then we're also going to use this constant. I'm not the this'd intensity constant, which is 10 times 10 to the minus 12 watts per meter squared. It's gonna be used in the definition of festivals. Okay, well, the first thing we weaken recognizes that the power which we're trying to calculate P is equal to the intensity times the area. Okay, well, the area is four pi r squared for hi r squared. Well, for empire. Obviously. Just constants are we know it's 9.0 meters. So we need to figure out the intensity so we can use the definition of vegetables which says that beta is equal to 10 timesthe log, which is a lot based in of the ratio of I mean since you were trying to find, we need to calculate power divided by that constant. I know. Okay. You know, Beta, we know why not. We need to find I. So we divide both sides by 10. And then we raised both sides to the 10th power because that's long based 10. So you get rid of the log rhythm, you have to raise both sides to the 10th power. So divine. Both but both sides by 10. And the race Both sides to the 10th power we have eye over, I not. It's equal to 10 to the beta over 10. Okay, solving for I I is equal to I know times 10 to the beta over 10. Well, beta is 115 115. Divided by 10 is 11.5. So this is 10 to the 11.5. Okay, well, plug that into the calculator. 10 of the 11.5 multiplied. Not by our constant I not which is 1.0 times. 10 to the minus 12. Three one, 662 You said watts per meter square. Uh oh. So now we know I so we can plug that into our relationship for power, which, again, P is equal to ay times four pi are square, so we plug in 0.3162 for I multiply that by four times Pi, uh, are square are being 9.0 meters and this is 322 lattes box set in. It's our solution.

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