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Waves - PowerPoint PPT Presentation

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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
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
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
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 wave1
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 wave2
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
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
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 waves1
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 waves2
Types of Waves
  • Longitudinal wave – the medium vibrates parallel to the direction of wave motion.
    • Examples – sound, slinky waves
wave energy
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 energy1
Wave Energy
  • For a spherical wave,
    • I = P/(4πr²)
      • I = intensity (in W/m²)
      • P = power
      • r = distance from wave source.
sample problem 2
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 is the bouncing of a wave off of a boundary.
  • Transmission is when a wave is able to pass through a boundary.
  • 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.
  • 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”
  • 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
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 waves1
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 waves2
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 waves3
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
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?
  • 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.