Chapter 7 WavesChapter 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 terminologyHarmonic 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 wavesRefraction (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 wavedirection bends, andwavelength 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 wavedirection bends, andwavelength shortens.

Sound bendingSound 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 channelingSound 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 scorpionsEarthquakes 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 togetherAdding 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 here

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 here

Resonance and standing wavesResonance 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) Standing waves in a plate (movie)

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) Standing waves in a plate (movie)

Galloping Gertie

Some wave leftoversSome wave leftovers Doppler effect -- frequency of waves is changed if

either source or observer is moving relative to the other (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.

Doppler effect -- frequency of waves is changed if either source or observer is moving relative to the other (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.