Chapter 10 & 11

Elasticity, Oscillations,

Waves, and Sound

Superposition of Waves

Superposition Principle – In the region where two or more waves overlap, the resultant is the algebraic sum of the various contributions at each point.

Example 19

Two speakers separated by a distance of 4.30 m emit sound of frequency 221 Hz. The speakers are in phase with one another. A person listens from a location 2.80 m directly in front of one of the speakers. Does the person hear constructive or destructive interference?

Solution:

Find the wavelength of the sound:

Find distance:

Find the diference of the distances:

Find the number of wavelengths in the distance:

This shows that there is destructive interference.

Example 20

Two speakers are opposite in phase. They are separated by a distance of 5.20 m and emit sound with a frequency of 104 Hz. A person stands 3.00 m in front of the speakers and 1.30 m to one side of the center line between them. What type of interference occurs at the person's location?

Solution:

Calculate the wavelength:

Find the distance from the speakers:

Find the difference in the paths:

Divide by the wavelength:

The person will experience constructive interference.

Sound Intensity

The Intensity (I) of a wave is the average energy delivered per unit area per unit time. Or the average power divided by the perpendicular area.

(18)

Units:

Example 21

A loudspeaker puts our 0.15 W of sound through a square area 2.0 m on each side. What is the intensity of this sound?

Solution:

Example 22

Two people relaxing on a deck listen to a warbler sing. One person, only 1.00 m from the bird, hears the sound with an intensity of . (a) What intensity is heard by the second person, who is 4.25 m from the bird? Assume that no reflected sound is heard by either person. (b) What is the power output of the bird's song?

Solution:

(a) Find the intensity at the second person:

(b) Find the power:

Intensity-Level

(19)

This equation gives you the decibel level (dB) of a sound.

Note: To double the loudness of a source, its intensity must be increased by a factor of ten. An increase of 10 dB in sound-level corresponds to a sound that's twice as loud.

Example 23

A crying child emits sound with an intensity of . Find (a) the intensity level in decibels for the child's sounds, and (b) the intensity level this child and its twin, both crying with identical intensities.

Solution:

(a)

(b)

On to Sound Part 4