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The amplitude of a sound wave is measured in terms of its maximum gauge pressure. By what factor does the amplitude of a sound wave increase if the sound intensity level goes up by 40.0 dB?

$F = 100$

Physics 101 Mechanics

Chapter 17

Physics of Hearing

Sound and Hearing

Cornell University

University of Washington

University of Winnipeg

Lectures

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thistles. Question number 24 from Chapter 17. This problem. We're given that the amplitude of a sound wave is measured in terms of max gauge pressure were then asked where you are then, given that the sound intensity level goes up by 40 decibels, and then we're asked to find the factor by which the amplitude of that sound wave increases. So this is similar new cup a problem we did a couple questions ago, but we have baited too minus beta. One. Just start with the basic relationship equals 40 and that just means that it's gone up 40 because beta two is 40 higher than beta one. So we just plug in our intensity equation into these Betas. It's now we conf accurate Factor out 10 and simplify this expression. So factor of 10 divide 10 over to the other side and we are left with long I to over I want equals four. Take the anti log of log and then raise 10. Raise 10 to the fourth Power is the anti log and we get I too over I won is equal to attend to the fourth. Okay, so this is our intensities, but we're dealing with amplitude here were asked to find the fact by which the amplitude increases. But we know that with this first day, my amplitude of a sound wave is measured in terms of Mac ex gauge pressure. That intensity is directly proportional to amplitude. So knowing that intensity is directly proportional to the amplitude, we can then make the statement that I to over I won. We write a better eye. Ah, to over I one is equal to x two over X one, and that whole is squared. And that comes from the gauge pressure. Um, the gauge pressure equation that has gauge pressure squared. OK, so we just found out that I, too over I want is 10 to the fourth. So now, 10 to the fourth we go to the next page so that I, too over i won is equal to attend to the fourth is equal to x two over X one amplitude that squared sound. We take the square root of both sides and that's gonna give us that X two over X one equals 100. And that means that the value of final amplitude increases by 100 times, so increases 100 times

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