Reflection Superposition Interference Wave Behavior Reflection Superposition Interference

Reflection Waves are reflected when they encounter a boundary of the medium Example: Rope tied to a wall - Reflection of Waves from Boundaries free boundary  Rope can move up and down fixed boundary  Rope cannot move at all At a free boundary, waves are reflected upright At a fixed boundary, waves are reflected inverted

Superposition Two waves can occupy the same medium at the same time (called superposition) They affect the medium independently The resultant wave is the sum of the displacements of the individual waves

Interference When two waves approach each other from opposite directions they combine in a way called interference When the displacements are in the same direction, constructive interference occurs When the displacements are in opposite directions, destructive interference occurs Transverse Waves-2

Sound

Sound Waves Sound waves are created by something vibrating: A sound wave is simply a pressure variation that is transmitted through matter Compression is where density and pressure are at a maximum (crest) Rarefaction is where density and pressure are at a minimum (trough) vibrating surface pressure waves

Sound Waves (cont.) Sound waves are longitudinal waves Sound waves usually propagate in three dimensions They create spherical wave fronts

Sound Waves (cont.) If you graph air pressure versus time, it looks like this:

Sound Waves (cont.) The speed of sound depends on the medium Air (25C): 346 m/s Water: 1490 m/s Sound waves cannot travel through a vacuum

Sound Waves (cont.) The speed of sound in air depends on temperature. The speed of sound in air at sea level at room temperature (20°C) is 343 m/s. Example: If you are 100 m from the crack of a bat striking a baseball, how long before you hear it? t = d/v = (100 m)/(343 m/s) = 0.29 s

Sound Waves (cont.) The loudness of sound is determined by the amplitude of the pressure wave. The pitch of sound is determined by the frequency of the wave. Humans can hear sounds between 20 Hz and 20,000 Hz (audible sound) Less than 20 Hz is called infrasound Greater than 20,000 Hz is called ultrasound

Beats Sound waves at slightly different frequencies produce beats The beat frequency is fbeat = |f1  f2|

Sound Intensity Intensity (I) is the rate of energy flow through a given area Intensity = Power/Area Intensity has units of W/m2 For a spherical wave: I =  where P = power output of the source r = distance from the source P 4 r2

Relative Intensity: Decibels The sensation of loudness is logarithmic with respect to intensity The decibel (dB) is a measure of the relative loudness of sound The reference intensity is the threshold of hearing, I0 = 1.0  10-12 W/m2 Decibel level (dB) = 10 log[I/I0] 0 dB is the threshold of hearing 120 dB is the threshold of pain

Doppler Shift Doppler shift is an apparent change in frequency caused by motion of the source relative to the receiver. When source and receiver are moving toward each other the sound has a higher frequency When source and receiver are moving away from each other the sound has a lower frequency.

Doppler Shift (cont.) Doppler shift is used to detect speed. Bats use the Doppler shift of sound to detect the speed of flying insects. Radar guns use the Doppler shift of radio waves to detect how fast someone is driving. Astronomers use the Doppler shift of light from distant galaxies to measure their speed and infer their distance.

Resonance All structures (strings, buildings, bridges, columns of air) have natural frequencies The natural frequencies correspond to standing waves in the structure The smallest natural frequency is called the fundamental frequency Resonance occurs when a periodic force acts on a structure at or near one of its natural frequencies A resonating structure can have very large oscillations and even break (Tacoma Narrows Bridge)

Standing Waves Standing waves form when a periodic wave interferes with its own reflection Standing waves form at only certain frequencies Nodes form where the displacement of the medium is zero Antinodes form where the displacement of the medium is maximum

Harmonics Harmonics are natural frequencies that are multiples of the fundamental frequency Each harmonic corresponds to a standing wave Example: vibrating string fn = n  n = 1, 2, 3, … Harmonics account for sound quality, or timbre v 2L

Standing Waves in an Air Column Standing waves can form in a tube of air If both ends are open, all harmonics are present fn = n  n = 1, 2, 3, … If one end is closed, only odd harmonics are present fn = n  n = 1, 3, 5,… v 2L v 4L