17.1

The principle of linear superposition states that when two or more waves are present simultaneously at the same place, the resultant disturbances from individual waves

17.2

Anytime two or more waves overlap in space an interference pattern results. The pattern may be very complicated if many waves of different amplitudes and frequency are involved. Constructive interference occurs when the waves are exactly in phase and destructive interference occurs when they are exactly out of phase.

Tow waves originally in a phase can get out of phase if they are required to travel different path lengths before combining. If one wave 1.2.3 travels farther than another than the two waves will be in phase and constructively interfere. If one wave ½, 3/2, 5/2 travels farther than the other the two waves will be out of phase and destructively interfere.

Constructive interference occurs at a point when two waves meet there crest-to-crest and trough-to-trough, thus reinforcing each other. Destructive interference occurs when the waves meet crest-to-trough and cancel each other

When waves meet crest-to-crest and trough-to-trough they are exactly in phase. When they meet crest-to-trough they are exactly out of phase

For two wave sources vibrating in phase, a difference in path lengths that is zero or an integer number of wavelengths leads to constructive interference: a difference in path lengths that is a half integer number (1.5,2.5) of wavelengths leads to destructive interference

For two wave sources vibrating out of phase, a difference in path lengths that is a half integer number of wavelengths leads to constructive interference; a difference in path lengths that is zero or an integer number of wavelengths leads to destructive interference

Example 1

Two in phase speakers are located 2.0 m apart and produce identical 550 Hz tones. A person stands 2.5 m from the left speaker and hears no sound. What are the possible distances of the person from the right speaker?

If the person hears no sound at all, completely destructive interference of the two sound waves arriving at his ear must be occurring. One of the sound waves must have traveled some odd multiple of λ/2 say n λ/2 farther than the other the difference in path length is sR=sL=n λ/2

Example 2

Two in phase radio towers 1.2 mi apart are broadcasting identical radio waves of frequency 550 kHz. Locate the points of constructive and destructive interference along the line that joins the two towers. Take the speed of radio waves to be 186,300 mi/s

17.3

Whenever a wave passes close to an obstacle or edge it bends around the object a process called diffraction. Phenomenon that lets you hear someone on other side of the house from you

All waves exhibit diffraction but sometimes the effect is so small that it escapes notice. Diffraction will be obvious when wavelength of wave is about same size as dimensions of obstacles it encounters. Why we hear diffraction of low frequency sound but don’t see diffraction of light

Diffraction is the bending of a wave around an obstacle or the edges of an opening. The angle through which the wave bends depends on the ration of the wavelength of wave to width D of opening; the greater the ration Y/D the greater the angle

When a sound wave of wavelength passes through an opening, the first place where the intensity of the sound is a minimum relative to that at the center of the opening is specified by angle theta.

If the opening is rectangular slit with width D such as a door way the angle is given by equation 17.1

If opening is circular with width D such as a loud speaker eq. 17.2

Example 3