# A trumpet creates a sound intensity level of 1.15 × 10 2 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.

### College Physics

11th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305952300

### College Physics

11th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305952300

#### Solutions

Chapter
Section
Chapter 14, Problem 18P
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.

Expert Solution

(a)

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

### Explanation of Solution

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

Expert Solution

(b)

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

Expert Solution

(c)

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

Expert Solution

(d)

To determine
The sound intensity level for first five trumpets

Expert Solution

(e)

To determine
Distance heard in the outdoor auditorium

Expert Solution

(f)

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

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