1.3 Introduction
1.3.1 Characteristics of Sound - Pressure Variations
1.3.2 Characteristics of Sound - Speed of Sound
1.3,3 Characteristics of Sound - Pitch Loudness and Timbre
1.3.4 Characteristics of Sound - Intensity
1.3.5 Doppler Effect
Unit 2.1 Multiple Choice Extended Questions - Waves
Unit 2.1 Multiple Choice Extended Answers-Waves
Unit 1.3 Multiple Choice Questions - Sound
Unit 1.3 Multiple Choice Answers - Sound

Unit 1.3 Sound Waves

Characteristics of Sound

1.3.4 Intensity of Periodic Sound Waves

pressure wave

Consider a point source emitting sound waves of power W, equally in all directions. This is a three dimensional wave called a spherical wave.


1. The air around the source is perfectly uniform

2. The sound is radiated in all directions equally

3. The speed of sound in all directions is the same

4. There are no sinks or other sources inside the sphere.



The wave spreads out so that the energy follows the inverse square law, so that r ∝ 1/A2 as illustrated in fig

By definition, the intensity I of a wave, or the power per unit area is the rate at which the energy transported by the wave transfers through a unit area A perpendicular to the direction of travel of the wave.

I = (Poweravg)/A

The energy emitted by the source passes through a sphere of radius r, so the average power emitted by the source must be distributed uniformly over each spherical wave front of area 4πr2.

Then Intensity becomes I = [Poweravg] /[4πr2]

The Intensity I follows the inverse square law, so that I ∝ 1/A2

Threshold of Hearing

At a frequency of 1 000 Hz, the faintest sounds the human ear can detect has an intensity of about 1.00 X 10-12 Wm-2, which is called threshold of hearing. and the loudest sounds without pain is about 1.00 Wm-2, which is called the threshold of pain.

Units of Sound Intensity

The human ear can detect a wide range of sound intensities so a linear scale is awkward and unmanageable. We use a logarithmic scale where the symbol β for sound intensity and Io as the reference intensity. Io is defined as the threshold of hearing and has the intensity 1.00 X 10-12 Wm-2.

β = 10 log [I/Io]

The intensity of sound β is measured in units called decibels (dB).

Loudness of a Sound

Loudness is the brains interpretation response to both the intensity and frequency of the sound. As a general rule an increase in sound level of 10 dB is interpreted as doubling of the loudness but is relatively inaccurate at very low or very high frequencies. The ear is not equally sensitive to all frequencies. The same loudness for sounds of different frequencies requires different intensities by the ear.

1. (a) My amplifier emits sound waves with an average output of 80.0W. Find the intensity at the neighbors fence 10.0 m from the source.

(b) Find the distance at which my sound can be heard.

(a) Answer = .....

(b) Answer = .....


2. (a) Calculate the sound level which causes pain [Hint... Intensity of 1.00 Wm-2 is called the threshold of pain].

(b) The EMA has measured the sound level experienced by runway workers from a jet plane as it lands is 150 dB. What is the sound intensity?

(a) Answer = .....

(b) Answer = .....


3. An 80 dB (decibel) sound is how many times stronger than a 40dB sound?

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Concept by Kishore Lal. Programmed by Kishore Lal... Copyright © 2015 Kishore Lal. All rights reserved.