Chapter 19 Vibrations and Waves Vibration A disturbance
Chapter 19 Vibrations and Waves
• Vibration: A disturbance “wiggle” in time. • Wave: A disturbance in space and time.
Oscillatory Motion • The to-and-fro vibratory motion, such as that of a pendulum.
Simple Pendulum For small displacements, the period of the simple pendulum is related to its length (L) and the acceleration due to gravity (g) by the following:
Simple Harmonic Motion • is a type of oscillatory motion in which the motion repeats itself. • This motion is caused by a “restoring force” that acts in the opposite direction of the displacement.
Simple Pendulum • Under small displacements, the simple pendulum behaves as a harmonic oscillator. • For a pendulum, the “restoring force” is usually exerted by GRAVITY
Amplitude • The maximum displacement from some equilibrium (mid point) position. (Applies to both vibrations and waves. )
Mass-Spring System is Another Example of a Simple Harmonic Oscillator Live Demonstration
Wavelength • The distance between successive crests, troughs, or identical parts of a wave. • Common symbol used for wavelength is the Greek letter - pronounced “lambda”
Sine Curve Crest Wavelength Trough Amplitude A
• Frequency: The number of vibrations per unit time. • Common symbols are f and the Greek letter - pronounced ”nu” • Period: The time in which a vibration is completed. • Common symbols are T and the Greek letter - pronounced “Tau”
More on frequency • We can talk about the frequency of a vibration or of a wave. Frequency is measured in inverse seconds, or Hertz (Hz). • E. g. . • f = 10 cycles/sec = 10 sec-1 = 10 Hz.
Frequency and Period are related • Frequency equals inverse Period. • Period equals inverse Frequency.
In symbols, this means. . . f = 1/T and T = 1/f or = 1/
Examples AM radio frequencies are measured in Kilo. Herts - (KHz). Kilo = one thousand = 1, 000 = 1 x 103. The period is 1/1, 000 Hz = 1 x 10 -3 sec = 1 millisecond (ms)
• FM radio frequencies are measured in Mega. Hertz (MHz) • Mega = one million = 1, 000 = 1 x 106 • The period is (1/1, 000 Hz)= 1 x 10 -6 sec = 1 microsecond ( s).
More Examples • Water waves might have a frequency of 2 Hz (i. e. 2 cycles per second). • The corresponding period is equal to: 1/f = 1/2 Hz = 0. 5 seconds
• The AM and FM radio waves are examples of • Electromagnetic Waves • Light is another example of an electromagnetic wave
The water waves are examples of Mechanical Waves Mechanical waves require a medium in which to propagate. Electromagnetic waves do not.
Wave Speed • The speed with which waves pass a particular point. • Common symbol used for wavespeed is the letter v.
• Wavespeed = wavelength / period • In symbols, this is: v = /T but, since we already know that frequency is the same as inverse period ( f = 1/T), then we can also write this as v = f
A note as to why we use “v” • The letter v is used for velocity in general. • Velocity and speed are closely related. • Velocity is speed in a specific direction.
For Example • If I tell you I’m traveling at 55 miles/hour due north, I have told you my velocity • If I tell you I’m traveling at 55 miles/hour, I have told you my speed.
Types of Waves There are two types of waves 1) Transverse Waves. 2)Longitudinal Waves.
1) Transverse Wave: A wave in which the vibration is in a direction perpendicular (transverse) to the direction in which the wave travels. e. g. Light waves. Waves on a string. Seismic “S”-waves.
2) Longitudinal Wave: A wave in which the medium vibrates in a direction parallel (longitudinal) to the direction in which the wave travels. e. g. Sound. Seismic P-waves. http: //www. physics. ohio-state. edu/133/demo/Lwave. gif
In a longitudinal wave, the medium has regions of compression and expansion which are along the direction of wave propagation. Regions of expansion are also called (rarefactions)
Interference A number of different waves can add, constructively or destructively. • This is known as superposition. The superposition of two or more waves results in interference.
Destructive Interference: Exactly out of Phase Cancellation + Zero displacement
Constructive Interference: Reinforcement + In Phase Maximum Displacement
Interference Pattern • The pattern formed by superposition of different sets of waves that produce mutual reinforcement in some places and cancellation in others. Superposition Principle of Wave
Standing Wave • A stationary wave pattern formed in a medium when two sets of identical waves pass through the medium in opposite directions. lecture demos
Standing Wave V Incident Wave V Reflected Wave V Standing Wave V
Beats • Sometimes, two waves with slightly different frequencies but the same amplitude can form the phenomenon known as beats. 15. 11 Beats
Blue colored wave + green colored wave ==> red colored wave. Two waves with same amplitudes but slightly different frequencies.
Doppler Effect • The shift in received frequency due to motion of a vibrating source toward or away from a receiver. 15. 6 The Doppler Effect
• Bow Wave The V-shaped wave made by an object moving across a liquid surface at a speed greater than the wave speed. (Since the source is moving faster than the wave speed, the wavefronts pile up. )
Shock Wave The cone-shaped wave made by an object moving at supersonic speed through a fluid. • (Here, the source is moving faster than the wave speed, which is the speed of sound!!) (Super-sonic speed)
Sonic Boom The loud sound resulting from the incidence of a shock wave. • (This is the result of the pile up of many wave fronts which produces a sonic boom)
Sonic Boom Piled up wave • fronts produce a shock wave Plane
Twice the speed of sound Mach 2 Wave front • 1 unit Plane 2 units
The End of Chapter 19
- Slides: 43