Chapter 7 Waves  Wave is a disturbance (usually in a material) that travels  EM wave (light) is an oscillating EM field, which needs no medium to travel in  Wave speed depends on properties of the medium (this is an important point) and sometimes slightly on wavelength  Transverse waves -- disturbance is perpendicular to wave velocity (e.g., light)  Longitudinal waves -- disturbance is in same direction as the wave velocity  Wave is a disturbance (usually in a material) that travels  EM wave (light) is an oscillating EM field, which needs no medium to travel in  Wave speed depends on properties of the medium (this is an important point) and sometimes slightly on wavelength  Transverse waves -- disturbance is perpendicular to wave velocity (e.g., light)  Longitudinal waves -- disturbance is in same direction as the wave velocity

Harmonic wave terminology  Amplitude -- size of wave  Wavelength ( ) -- distance between peaks  Period (T) -- time for one cycle  Frequency (f = 1/T) -- number of cycles per second. 1 cycle/sec = 1 Hz  Wave travels one wavelength in one period  Speed of wave v = /T = f  Harmonic waves show up in music, optics, earthquakes, even quantum mechanics  Amplitude -- size of wave  Wavelength ( ) -- distance between peaks  Period (T) -- time for one cycle  Frequency (f = 1/T) -- number of cycles per second. 1 cycle/sec = 1 Hz  Wave travels one wavelength in one period  Speed of wave v = /T = f  Harmonic waves show up in music, optics, earthquakes, even quantum mechanics

Refraction (bending) of waves  Remember: wave speed depends on properties of the medium  If properties differ in space, wave will have different speed in different places  For example, light wave goes from air to water. Speed is slower in water, so wave direction bends, and wavelength shortens.  Remember: wave speed depends on properties of the medium  If properties differ in space, wave will have different speed in different places  For example, light wave goes from air to water. Speed is slower in water, so wave direction bends, and wavelength shortens.

Sound bending  Sound waves have higher speed at higher T  So a wavefront will bend toward lower temperature regions  Sometimes in the evening, a temperature inversion will form: cooler air near the ground, warmer air above  Sounds waves bend toward the ground, so sounds in the evening can be heard from a considerable distance.  Sound waves have higher speed at higher T  So a wavefront will bend toward lower temperature regions  Sometimes in the evening, a temperature inversion will form: cooler air near the ground, warmer air above  Sounds waves bend toward the ground, so sounds in the evening can be heard from a considerable distance.

Sound channeling  Sound speed in ocean reaches a minimum at a depth near 1 km -- sofar spheres  Sound speed in atmosphere reaches a minimum around 50,000 feet -- the “flying disk” of Roswell fame All because 1) speed depends on properties of the medium and 2) sound waves bend toward regions where sound speed is lower  Sound speed in ocean reaches a minimum at a depth near 1 km -- sofar spheres  Sound speed in atmosphere reaches a minimum around 50,000 feet -- the “flying disk” of Roswell fame All because 1) speed depends on properties of the medium and 2) sound waves bend toward regions where sound speed is lower

Earthquakes and scorpions  First the P-wave (longitudinal)  Then the S-wave (shear; not in liquids)  Then the L-wave (long, rolling, surface wave) P-wave almost twice as fast as S- or L-wave Scorpions get direction to prey from P- or S- wave, but they get distance from time delay between the two waves.  First the P-wave (longitudinal)  Then the S-wave (shear; not in liquids)  Then the L-wave (long, rolling, surface wave) P-wave almost twice as fast as S- or L-wave Scorpions get direction to prey from P- or S- wave, but they get distance from time delay between the two waves.

Adding waves together  Individual waves just add together  Now the phase of each wave matters  Phase is like the sweep hand on a clock -- once around the clock = one cycle  When waves have different phases (caused by lots of things), they interfere -- positive or negative (they add or subtract)  Interference is IMPORTANT  Check out simulation of beats here or herehere  Individual waves just add together  Now the phase of each wave matters  Phase is like the sweep hand on a clock -- once around the clock = one cycle  When waves have different phases (caused by lots of things), they interfere -- positive or negative (they add or subtract)  Interference is IMPORTANT  Check out simulation of beats here or herehere

Resonance and standing waves  Every oscillatory system has a natural frequency  Add energy at this frequency, and it builds up in the system until something stops it  Musical instruments of all types  Standing waves in a string  Fundamental and harmonic frequencies  Slowly change the driving frequency (movie)movie  Standing waves in a plate (movie)movie  Galloping Gertie Galloping Gertie  Every oscillatory system has a natural frequency  Add energy at this frequency, and it builds up in the system until something stops it  Musical instruments of all types  Standing waves in a string  Fundamental and harmonic frequencies  Slowly change the driving frequency (movie)movie  Standing waves in a plate (movie)movie  Galloping Gertie Galloping Gertie

Some wave leftovers  Doppler effect -- frequency of waves is changed if either source or observer is moving relative to the other (movie)movie  Huygen’s principle and the bending of waves -- Think of each point on a wave as a tiny source of new circular waves. This allows waves to “bend” around corners and interfere with different parts of itself  Helps explain some interference phenomena. Think of these two wave sources as a single wave going through two slits.these two wave sources  Doppler effect -- frequency of waves is changed if either source or observer is moving relative to the other (movie)movie  Huygen’s principle and the bending of waves -- Think of each point on a wave as a tiny source of new circular waves. This allows waves to “bend” around corners and interfere with different parts of itself  Helps explain some interference phenomena. Think of these two wave sources as a single wave going through two slits.these two wave sources