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?



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?



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.





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?




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?



(a) Find the intensity at the second person:

(b) Find the power:





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.





On to Sound Part 4