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Waves. What are waves?. Wave –A disturbance that transfers energy through a medium without net motion of the medium. Mechanical Wave – a wave that propagates through a deformable, elastic medium Waves can be represented by a sine wave. Types of waves.
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What are waves? • Wave –A disturbance that transfers energy through a medium without net motion of the medium. • Mechanical Wave – a wave that propagates through a deformable, elastic medium • Waves can be represented by a sine wave.
Types of waves • Pulse wave – a single, non-periodic disturbance. • Periodic or continuous wave – a wave whose source is some form of repeating motion.
Parts of a wave • Crest – highest point above equilibrium. • Trough – lowest point below equilibrium. • Amplitude – maximum height of a crest or depth of a trough.
Parts of a wave • Wavelength – the distance between two adjacent crests or troughs. • Frequency – number of crests (or troughs) that pass by a point in a given amount of time. • Period – Time for two adjacent crests to pass by a certain point.
Parts of a wave • Wave velocity – velocity at which wave crests move. • v = λf • v = wave velocity • λ = wavelength • f = frequency
Speed of waves on cords • v = √[T/(m/L)] • v = velocity of a wave • T = tension in cord • m = mass of cord • L = length of cord
Sample problem 1 • A wave whose wavelength is 0.30 m is traveling down a 300 m long wire whose total mass is 15 kg. If the wire is under a tension of 1000 N, what are the speed and frequency of this wave?
Types of Waves • Waves can be categorized by how the medium moves in relation to the wave motion. • Transverse wave – wave propagates perpendicular to the direction the medium vibrates. • Examples – water waves, light, “the wave”
Types of Waves • Longitudinal wave – the medium vibrates parallel to the direction of wave motion. • Examples – sound, slinky waves
Wave Energy • The amount of energy carried by a wave is proportional to the square of the amplitude. • Intensity – power transported across unit area perpendicular to the direction of energy flow.
Wave Energy • For a spherical wave, • I = P/(4πr²) • I = intensity (in W/m²) • P = power • r = distance from wave source.
Sample Problem 2 • The intensity of an earthquake P wave traveling through the Earth and detected 100 km from the source is 1.0 x 10⁶ W/m². What is the intensity of that wave if detected 400 km from the source?
Reflection • Reflection is the bouncing of a wave off of a boundary. • Transmission is when a wave is able to pass through a boundary.
Interference • Interference is what happens when two waves pass through the same region of space at the same time. • Where waves overlap, the resultant displacement is equal to the sum of their separate displacements.
Interference • This is called the principle of superposition. • Interference can be either constructive or destructive. • Constructive interference – results when waves on the same side of equilibrium add together to form a larger displacement. • Can be said to be “in phase”
Interference • Destructive interference – results when waves on opposite sides of equilibrium combine to form a smaller displacement. • Can be said to be “out of phase”
Standing Waves • A standing wave is a wave that appears to only move up and down. • Occurs when waves of a certain wavelength and frequency interfere with each other. • Have nodes and antinodes.
Standing Waves • Nodes are the part of a standing wave with no motion. • Always has complete destructive interference. • Antinodes are the part of a standing wave where the maximum amplitude occurs. • Only spot where complete constructive interference occurs.
Standing Waves • Only a certain set of frequencies will produce standing waves on a string. • For a string, only frequencies where the length of the string is equal to a ½ multiple of the wavelength produce standing waves.
Standing Waves • Fundamental frequency or 1st harmonic: L = ½λ₁ • First overtone or 2nd harmonic: • L = λ₂ • Second overtone or 3rd harmonic: • L = ³∕₂λ₃
Sample Problem 3 • A piano string is 1.10 m long and has a mass of 9.00 g. (a) How much tension must the string be under if it is to vibrate at a fundamental frequency of 131 Hz? (b) What are the frequencies of the first four harmonics?
Resonance • When the external frequency of a vibration matches a resonant frequency of another object, the second object will start to vibrate. • This is called resonance. • Example: when you push a swing.
