Waves

Wave Properties Waves are propagated by a vibrating source Pulse – single disturbance created by a single oscillation Periodic Wave – periodic disturbance created by a continuously vibrating source

Definition Mechanical Wave - transfer of energy through a medium Waves can move over large distances, but the particles of the medium only vibrate about fixed positions Waves transport energy but not matter Mechanical waves must travel through a medium

Types of Waves Transverse – particles in medium vibrate perpendicular to the direction of the wave motion A crest trough

Crest – max displacement Trough – minimum displacement λ – wavelength – distance between two successive crests (or troughs) A – amplitude – maximum displacement from the rest position

Longitudinal Waves Particles vibrate parallel to the direction of wave motion

Compression – wave particles are compacted closely together Rarefaction – where particles are spread out Wavelength – distance between two corresponding in phase points Amplitude – maximum displacement from rest

Damping Initial amplitude of the wave depends on the initial energy of the source Energy decreases over time, so the amplitude does as well - damping

Wave Equation The velocity of a wave is related to its wavelength and frequency Velocity – speed the wave travels Frequency – number of cycles that pass a given point per second (in Hertz) - measured by crests per second v = λf

Example A wave has a wavelength of 5m and a frequency of 3 Hz. What is its speed? A crest of a wave in a pool takes 2.5sec to travel from one end to the other end (20m). It is noticed that 10 crests pass by a mark in 15 sec. What is the wavelength?

The frequency of a wave is determined by the rate that the source produces them The velocity of a wave depends on the properties of the medium

Velocity of Transverse In transverse waves the velocity depends on the tension (tightness) of the medium and the mass/length of the medium Greater tension increase both v and f v = √(F t /(m/L))

Example A wave of wavelength.30m is traveling down a 300m long wire of mass 15kg. If the wire is under a tension of 1000N, what is the velocity and frequency of the wave?

Longitudinal Velocity Velocity in longitudinal waves depends on the elasticity(E) of the material and the density(ρ) of the material v = √(E/ ρ)

Example You can hear a train approaching by putting your ear to the track. How long does it take for a sound wave to travel 1.0km down a steel track? E = 2.0x10 11 N/m 2 and ρ = 7.8x10 3 kg/m 3