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Chapter 19: Problem 19

Estimate the maximum possible sound level in decibels of sound waves in air. (Hint: Set the pressure amplitude equal to \(1 \mathrm{~atm} .\) )

Short Answer

Expert verified
The maximum possible sound level in air is approximately 194 dB.

Step by step solution

01

Understanding the Given Information

It's given that the pressure amplitude is set as 1 atm. We also know that 1 atmosphere (atm) is equivalent to \(1.013 \times 10^{5}~\mathrm{Pa}\). Moreover, the reference pressure (\(p_0\)) for sound in air is specified as \(2 \times 10^{-5}~\mathrm{Pa}\).
02

Apply the Formula for Sound Level in Decibels

The formula for calculating the sound level in decibels is given by \(L = 20 \log \left(\frac{p}{p_0}\right)\) where \(p\) is the pressure amplitude and \(p_0\) is the reference pressure. The pressure amplitude in this case is equivalent to \(1.013 \times 10^{5}~\mathrm{Pa}\) and the reference pressure is \(2 \times 10^{-5}~\mathrm{Pa}.\)
03

Substitute the Values into the Formula

Substitute the values of \(p\) and \(p_0\) into the formula, it gives:\[L = 20 \log \left(\frac{1.013 \times 10^{5}}{2 \times 10^{-5}}\right)\]
04

Calculate the Sound Level

On calculating the value in the logarithmic part of the expression by dividing \(1.013 \times 10^{5}\) by \(2 \times 10^{-5}\), it results in \(5.065 \times 10^{9}\). Taking the logarithm gives 9.70. Multiplying 9.70 by 20 gives a sound level of 194 dB.

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Most popular questions from this chapter

The pressure in a traveling sound wave is given by the equation $$ \Delta p=(1.48 \mathrm{~Pa}) \sin [(1.07 \pi \mathrm{rad} / \mathrm{m}) x-(334 \pi \mathrm{rad} / \mathrm{s}) t] $$ Find \((a)\) the pressure amplitude, (b) the frequency, \((c)\) the wavelength, and \((d)\) the speed of the wave.

Diagnostic ultrasound of frequency \(4.50 \mathrm{MHz}\) is used to examine tumors in soft tissue. \((a)\) What is the wavelength in air of such a sound wave? \((b)\) If the speed of sound in tissue is \(1500 \mathrm{~m} / \mathrm{s}\), what is the wavelength of this wave in tissue?

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