   Chapter 14, Problem 18P

Chapter
Section
Textbook Problem

A trumpet creates a sound intensity level of 1.15 × 102 dB at a distance of 1.00 m. (a) What is the sound intensity of a trumpet at this distance? (b) What is the sound intensity of five trumpets at this distance? (c) Find the sound intensity of five trumpets at the location of the first row of an audience, 8.00 m away, assuming, for simplicity, the sound energy propagates uniformly in all directions. (d) Calculate the decibel level of the five trumpets in the first row. (e) If the trumpets are being played in an outdoor auditorium, how far away, in theory, can their combined sound be heard? (f) In practice such a sound could not be heard once the listener was 2-3 km away. Why can’t the sound be heard at the distance found in part (e)? Hint: In a very quiet room the ambient sound intensity level is about 30 dB.

(a)

To determine
The sound intensity of a trumpet at a distance of 1m.

Explanation

Given Info: The intensity level of sound of a trumpet is 1.15×102dB at a distance of 1.00 m.

Formula to calculate the sound intensity of a trumpet is,

β=10log(II0)

• I0 is reference Intensity,
• I is the intensity of a trumpet,

Simplify and rearrange the expression in terms of I .

β10=log(II0)10β10=(II0)I=I010β10

The value of reference intensity constant is 1.0×1012W/m2

Substitute 1

(b)

To determine
The sound intensity of a five trumpet at a distance of 1m.

(c)

To determine
The sound intensity of five trumpets at a location.

(d)

To determine
The sound intensity level for first five trumpets

(e)

To determine
Distance heard in the outdoor auditorium

(f)

To determine
Why the sound can be heard at a large distance.

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