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