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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: (III) When a player’s finger presses a guitar string down onto a fret, the length of the vibrating portion of the string is shortened, thereby increasing the string’s fundamental frequency (see Fig. 12–36). The string’s tension and mass per unit length remain unchanged. If the unfingered length of the string is l= 75.0 cm, determine the positions x of the first six frets, if each fret raises the pitch of the fundamental by one musical note compared to the neighboring fret. On the equally tempered chromatic scale, the ratio of frequencies of neighboring notes is 21/12.

Figure 12-36

When a sound wave passes from air into water, what properties of the wave will change?

(a) Frequency.

(b) Wavelength.

(c) Wave speed.

(d) Both frequency and wavelength.

(e) Both wave speed and wavelength.

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: Two identical tubes, each closed one end, have a fundamental frequency of 349 Hz at \({\bf{25}}.{\bf{0^\circ C}}\). The air temperature is increased to \({\bf{31}}.{\bf{0^\circ C}}\) in one tube. If the two pipes are now sounded together, what beat frequency results?

(II)An ocean fishing boat is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.55 km away (Fig. 12-33). How much time elapses before the backfire is heard (a) by the fish, and (b) by the fishermen?
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