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Chapter 16: Q. 36 (page 452)

During takeoff, the sound intensity level of a jet engine is 140 dB at a distance of 30 m. What is the sound intensity level at a distance of 1.0 km?

Short Answer

Expert verified

The sound intensity level at a distance of $1.0 k m$ is $110 d B$ .

Step by step solution

01

Given information

Intensity level of a jet engine is $β = 140 d B$

Distance $1.0 k m = 1000 m$

02

Sound intensity at 1.0 km

The sound intensity at $1.0 k m$ is

$I' = (\frac{30 m}{1000 m}) I I' = (\frac{3}{100}) I$

03

Sound intensity level at 1.0 km

The sound intensity level is given by $β = (10 d B) \log_{10} (\frac{I'}{I_{0}})$ .

Substitute the given values

$β' = (10 d B) \log_{10} (\frac{{(\frac{3}{100})}^{2} I}{I_{0}}) β' = (10 d B) \log_{10} {(\frac{3}{100})}^{2} + (10 d B) \log_{10} (\frac{I}{I_{0}}) β' = - 30 d b + 140 d B β' = 110 d B$

Therefore, the sound intensity level at a distance of $1.0 k m$ is $110 d B$ .

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Most popular questions from this chapter

A wave on a string is described by $D (x, t) = (3.0 c m) \times \sin [2 π (\frac{x}{2.4 m}) + t / (0.20 s) + 1]$ , where x is in m and t is in s.

a. In what direction is this wave traveling?

b. What are the wave speed, the frequency, and the wave number?

c. At t = 0.50 s, what is the displacement of the string at

x = 0.20 m?

What are the amplitude, wavelength, frequency, and phase constant of the traveling wave in FIGURE Q16.7?

The sun emits electromagnetic waves with a power of 4.0 * 1026 W. Determine the intensity of electromagnetic waves from the sun just outside the atmospheres of Venus, the earth, and Mars.

One cue your hearing system uses to localize a sound (i.e., to

tell where a sound is coming from) is the slight difference in the

arrival times of the sound at your ears. Your ears are spaced

approximately 20 cm apart. Consider a sound source 5.0 m from

the center of your head along a line 45 to your right. What is the

difference in arrival times? Give your answer in microseconds.

Hint: You are looking for the difference between two numbers that are nearly the same. What does this near equality imply about the necessary precision during intermediate stages of the calculation?

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0.50% longer than the corresponding wavelengths measured in a terrestrial laboratory. Is the galaxy approaching or receding from the earth? At what speed?

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