1. WAVES l wave = disturbance that propagates “disturbance” e.g., displacement of medium element from its equilibrium position; propagation can be in medium or in space (disturbance of a “field”); l mechanical waves: when matter is disturbed, energy emanates from the disturbance, is propagated by interaction between neighboring particles; this propagation of energy is called wave motion; a traveling mechanical wave is a self-sustaining disturbance of a medium that propagates from one region to another, carrying energy and momentum. examples:  waves on strings,  surface waves on liquids,  sound waves in a gas (e.g. in air),  compression waves in solids and liquids; it is the disturbance that advances, not the material medium transverse wave displacements perpendicular to direction of propagation; longitudinal wave sustaining medium displaced parallel to direction of propagation (e.g. sound waves, some seismic waves, compression waves in a bell);

2. periodic wave motion l periodic wave motion: particles oscillate back and forth, same cycle of displacement repeated again and again; (we only discuss periodic waves) l terms describing waves: crest of the wave = position of maximum displacement (“highest point of the wave”) amplitude = amount of maximum displacement (height of crest above undisturbed position) wave velocity v = velocity of propagation of wave crest wavelength = distance between successive same- side crests frequency f = number of same-side crests passing by a fixed point per second period T = time for one complete wave oscillation: period = 1/frequency unit of frequency: 1 hertz = 1Hz = 1/second wave velocity (speed of waves) depends on properties of the carrying medium; in general: speed of mechanical waves in solids greater than in liquids, and greater in liquids than in gases. relation between speed, wavelength and frequency: v = f, i.e. speed = frequency times wavelength

3. Energy in a wave l intensity of a wave is a measure of how much power is transported to a point by the wave; intensity = energy flow per unit time, per unit area = power per unit area, (where area = area perpendicular to propagation direction) energy flow carried by wave: is proportional to the square of the amplitude and the square of the frequency; “ inverse square law of wave intensity ”: the intensity of a wave is inversely proportional to the square of the distance from the source of the wave I = P/(4  R 2 ) (source = object emitting the wave) (I = intensity, P = total power emitted by source, R = distance from source) (strictly speaking, only for point-like or spherically symmetric sources, or if size of the source much smaller than R)

4. Superposition of waves, interference l Superposition principle: two or more waves moving through the same region of space will superimpose and produce a well- defined combined effect; the resultant of two or more waves of the same kind overlapping is the algebraic sum of the individual contributions at each point, i.e. the (signed) displacements (elongations) add. l Huygens' principle every point on a wavefront can be considered as a source, emitting a wave; the superposition of all these waves results in the observed wave. consequences: interference, diffraction interference: superposition of two waves of same frequency can lead to reinforcement (constructive interference) or partial or complete cancellation (destructive interference; constructive interference: two waves “in phase”, (i.e. crests of two waves coincide in time) reinforce each other, resultant amplitude bigger than that of individual waves; destructive interference: two waves “completely out of phase” (i.e. out of phase by 1/2 period, so that crests of one wave coincide with troughs of the other)  cancellation; complete cancellation (extinction) if both waves have same amplitude.

5. Interference, cont’d l phase differences can be caused by: differences in pathlength; given a pathlength difference, the phase difference depends on the wavelength; travel time difference due to difference in speed in different media; reflection; l examples: colors of thin films (oil on water, soap bubbles) dead spots in auditorium diffraction grating:  many narrow parallel slits spaced closely together;  every slit forms source for wave;  differences in pathlength from different slits to some point in space  phase difference  wavelength dependent interference pattern;  can be used to measure wavelength; interferometers:  Michelson - Morley (used to measure “ether wind”)  Fabry - Perot

6. SOUND l Sound waves propagate in any medium that can respond elastically and thereby transmit vibrational energy. l sound waves in gases and liquids are longitudinal (alternating compression and rarefaction); in solids, both longitudinal and transversal; l speed of sound is independent of frequency; l speed of sound in air  340m/s at 20 o C; increases with temperature;  1500m/s in water; l three frequency ranges of sound waves: below 20 Hz: infrasonic 20 Hz to 20 kHz: audible, i.e. sound proper above 20 kHz: ultrasonic, “ultrasound” l pitch is given by frequency e.g. “standard a” corresponds to 440 Hz l intervals between tones given by ratio of frequencies (e.g. doubling of frequency - one octave) l male voice range 80 Hz to 240 Hz for speech, up to 700 Hz for song; l female voice range 140 Hz to 500 Hz for speech, up to 1100 Hz for song.