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Chapter 12: Q91GP (page 328)

Question: A sound-insulating door reduces the sound level by\({\bf{30}}\,{\bf{dB}}\). What fraction of the sound intensity passes through this door?

Short Answer

Expert verified

The \(\frac{1}{{1000}}\) sound intensity passes through the door.

Step by step solution

01

Concept

The equation of sound intensity is,

\(\beta = 10\log \frac{I}{{{I_0}}}\)

The intensity of the emitted sound is\(I\)and the intensity of the threshold audible sound is\({I_0} = {10^{ - 12}}\;{\rm{W/}}{{\rm{m}}^{\rm{2}}}\).

02

Given Data

The sound decreases by \(\beta = - 30\;{\rm{dB}}\).

03

Calculation

The intensity decreases as it passes through the door. So you can write,

\(\begin{array}{c}\beta = 10\log \frac{I}{{{I_0}}} = - 30\\\log \frac{I}{{{I_0}}} = - 3\\\frac{I}{{{I_0}}} = {10^{ - 3}}\\\frac{I}{{{I_0}}} = \frac{1}{{1000}}\end{array}\)

Hence, the\(\frac{1}{{1000}}\) sound intensity passes through the door.

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Most popular questions from this chapter

Question: Manufacturers typically offer a particular guitar string in a choice of diameters so that players can tune their instruments with a preferred string tension. For example, a nylon high-E string is available in a low- and high-tension model with diameter 0.699 mm and 0.724 mm, respectively. Assuming the density \(\rho \) of nylon is the same for each model, compare (as a ratio) the tension in a tuned high-and-low tension string.

A fireworks shell explodes 100 m above the ground, creating colorful sparks. How much greater is the sound level of the explosion for a person at a point directly below the explosion than for a person a horizontal distance of 200 m away (Fig. 12-34)?

Question: A dramatic demonstration, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For an \({\bf{80}}\)-cm-long rod, (a) what is the fundamental frequency of the sound? (b) What is its wavelength in the rod, and (c) what is the traveling wavelength of the sound in air at\({\bf{2}}{{\bf{0}}^{\bf{o}}}{\bf{C}}\)?

To make a given sound seem twice as loud, how should a musician change the intensity of the sound?

(a) Double the intensity.

(b) Halve the intensity.

(c) Quadruple the intensity.

(d) Quarter the intensity.

(e) Increase the intensity by a factor of 10.

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridge?

FIGURE 12–30 Question 9.
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