Waves Wave Properties Waves are propagated by a

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 crest A 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 5 m and a frequency of 3 Hz. What is its speed? • A crest of a wave in a pool takes 2. 5 sec to travel from one end to the other end (20 m). 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 = √(Ft/(m/L))

Example • A wave of wavelength. 30 m is traveling down a 300 m long wire of mass 15 kg. If the wire is under a tension of 1000 N, 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. 0 km down a steel track? E = 2. 0 x 1011 N/m 2 and ρ = 7. 8 x 103 kg/m 3