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PHYS1000 Waves 1

Waves

What is a wave? A wave is a disturbance moving through a medium.

If the disturbance consists of motion of the medium, the medium moves back and forth aboutits usual resting position the material the medium is made up of does not ow. Waves onwater move along the surface, even though the water itself only moves up and down.

The wave carries energy from one place to another. Again, consider water waves. You canproduce waves by moving a oating object up and down. The waves will spread out, and canmake other oating objects move transferring energy to them.

Types of waves

Type of motion

transverse waves:the disturbance is at right angles to the direction the wave travels in

motion of wavemotion of

medium

example: waves moving along a stretched string, water waves

longitudinal waves:the disturbance is parallel to the direction the wave travels in

motion of wave

motion of medium

example: sound waves

Behaviour over time

pulse: brief disturbance

periodic wave: repeats continuously

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Periodic waves

A periodic wave consists of a repeating pattern:

distance: wavelength

peaktopeak

amplitude

1 repeating cycle

time: period T

The wave can be described by the shape of the disturbance, the period T or frequency f , and thewavelength . The wavelength is the length of the repeating cycle.The speed of the wave, and the frequency and wavelength are related by

v = f

Harmonic wavesA harmonic wave is described by:

y = A sin (2

x 2 f t + )

distance: wavelength

1 repeating cycle

time: period T

peaktopeak

amplitude

peakamplitude

A

has the shape of a sine curve also called a sine wave the mathematically simplest wave EXTRA any wave of any shape can be produced by adding harmonic waves together (Fourier

theorem) can also write as A cos (. . .) the formula above is in radians we can use degrees if we want:

y = A sin (360 x/ 360 f t + )

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Properties of waves

superposition:

We can add two waves by adding the disturbances of each wave together. If the two waves areperiodic, with the same wavelength and frequency, the effect will be the same over time (at agiven point) we have interference

constructive interference:two waves add together to give a larger wave

destructive interference:two waves partly or completely cancel

reection:when the wave reaches a boundary with another medium, some of the wave is reected back-wards into the original medium

refraction:when a waves passes through a boundary with another medium, the direction can change

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ADVANCED diffraction:if a wave travels through a small gap, it spreads out