11-3: PROPERTIES OF WAVES

Wave Motion A wave is a disturbance created by a vibrating source. Two types of waves Electromagnetic or Mechanical Electromagnetic waves can travel through space Mechanical waves require a material medium.

As a wave propagates, particles in the medium vibrate about an equilibrium position.

Wave Types Pulse - is a single non periodic disturbance. Periodic wave - a wave whose source is undergoing some form of periodic motion.

Transverse waves Particles vibrate at right angles to the direction of propagation. Crest – the highest point above the equilibrium position Trough – the lowest point below the equilibrium position Wavelength – the distance between two adjacent similar points of the wave, symbol = 

Longitudinal waves Particles vibrate parallel to the direction of wave motion. The crests of the wave corresponds to the compressed regions, and the trough corresponds to the stretch regions

Graphs of Waves

Frequency & Period The frequency of a wave is the number of crests that pass a point in a given time (usually in hertz). The period is the time required for the wave to travel one wavelength (two successive crests).

Wave Speed The relationship between the frequency and wavelength of a wave is given by the wave equation: Energy carried by a wave depends on the amplitude at which the particles of the medium are vibrating. As the amplitude increases so does the energy the wave carries

Sample Problem The string of a piano that produces the note middle C vibrates with a frequency of 264Hz. If the sound waves produced by this string have a wavelength in air of 1.30 m, what is the speed of sound in air?

Solution Given: Frequency = 264 Hz wavelength = 1.30 m v = ? v = frequency x wavelength = 264 Hz x 1.30 m = 343 m/s

Sample Problem 2 boats are anchored 4 m apart. They bob up & down every 3 s. When one is up, the other is down. There are no crests between them. Determine the speed of the waves.

½ = 4 m  = 8m f = 1/T = 1/3s = 0.33 s-1 v = f = (8m)(0.33 s-1) = 2.7 m/s

11-4 Wave Interactions

Superposition Superposition is the idea that two waves can occupy the same space at the same time. Superposition principle: when two or more waves travel through a medium, the resultant wave is the sum of the displacements of the individual waves at each point.

Once the waves pass through each other each wave proceeds independently.

Constructive Interference Results when 2 waves meet up exactly crest to crest ( in phase). This produces a pulse of greater amplitude than either of the original waves.

Destructive Interference Results when two waves meet exactly crest to trough ( out of phase). If the individual waves have the same amplitude the resultant wave will equal zero.

Reflection from Free and Fixed Boundaries

Standing Waves Wave pattern that results when two identical waves travel in opposite directions and interfere.

Node: point in a standing wave that always undergoes complete destructive interference and therefore is stationary Antinode: point in a standing wave, halfway between two nodes, at which the largest amplitude occurs

Only certain frequencies produce standing waves. The wavelengths depend on the string length. Possible wavelengths include 2L, L, and (2/3)L