waves

definition

A wave is a wiggle in space and time.A wave is an oscillation (a repeated disturbance).

what does the waving?

1. mechanical waves the wave disturbance occurs in a medium (substance)e.g., pressure disturbance in air (sound waves) disturbance of water surface (water waves)

2. electromagnetic wavesrequire no mediume.g., light, x-rays

There are two directions associated with waves.

1. propagation direction

Where the wave goes.Where the energy goes.

what direction is the waving done in?

2. oscillation direction

The direction in which individual particles (or fields) move.

If propagation and oscillation are at right angles, it’s a transverse wave.

oscillationpropagation

wave on a string (PHeT)

crowd doing the wave (video)

There were once water ripples on Mars.

Some bats can detect the

ripples made by frogs when

calling for mates.

The ripples are like a target,

with a juicy meal at the center!

Anatomy of a transverse wave

wavelength

wavelength = horizontal distance between any two identical points on the wave. Units: m Symbol: (“lambda”)

Anatomy of a transverse wave

amplitude

amplitude = vertical distance from center line to wave peak. Units: m

If propagation and oscillation are in the same direction, it’s a longitudinal wave.

oscillation propagation

ancient video on sound

slinky

Anatomy of a longitudinal wave

compression = region of high pressure

rarefaction = region of low pressure

high pressure low pressure

Anatomy of a longitudinal wave

wavelength

wavelength = horizontal distance between any two identical pressures. Units: m Symbol:

compression rarefaction

amplitude = maximum pressure – average pressure.

pre

ssure

amplitude

avera

ge

the wave equation

frequency = number of waves passing a fixed point each second.

Symbol: f

Units: Hz (“Hertz”)

the wave equationLet’s count the number of waves passing in 1 sec:

t = 1 s

t = 0 s

2.25 waves

the wave equation

frequency = number of waves passing a fixed point each second.

f = 2.25 Hz in the example from the previous slide.

the wave equationWe can also calculate the frequency if we know the wave’s speed, .

t = 1 s

𝑑

𝑑=𝑣𝑡

the wave equationWe can also calculate the frequency if we know the wave’s speed, .

t = 1 s

𝑑number of wavelengths

𝜆

the wave equation

number of wavelengths

frequency = number of wavelengths in 1 sec, so set = 1 sec:

Therefore,

or

the wave equation

the wave equation

the wave equationExample1. What is the frequency of red light?

(=700 nm, speed of light = 2.99 x 108 m/s)

Make sure everything’s in SI units:

Solve: , therefore