Waves

What Are Waves?Wave – a disturbance that transfers energy

-- the energy transferred through a wave can be carried from the disturbance, through the wave, to another object

Ex: wind gives energy (a disturbance), creating waves on an ocean, and the ocean carries that energy to a boat, and the energy rocks the boat up and down

-- the energy from the disturbance is transferred through a medium

MediumsMedium – the substance through which a wave travels

-- in an ocean wave, water is the medium

-- in sound waves, air is the medium

It is important to understand that the wave DOES NOT CARRY the medium itself. It only moves energy through the medium.

-- the ship doesn’t move on the waves, it only bobs up and down

What Causes Waves?Waves are created when a source of energy causes a vibration in a medium

Vibration – a repeated back-and-forth or up-and-down motion

-- some mediums can vibrate a lot with only a little energy input

-- other mediums only vibrate a little with a lot of energy input

-- the amount of vibration depends on the spacing and type of molecules within the medium

Types of WavesThere are three different types of waves, which are solely characterized by the way that they move.

The three types of waves are:

-- Transverse waves

-- Longitudinal Waves

-- Surface Waves

Transverse WavesTransverse waves – waves whose mediums move a right angles (perpindicular) to the direction of overall wave travel

-- if the wave below moves left-to-right, the medium will move up-and-down

-- like whipping a rope

Parts of a Transverse Wave

Crest – the “high” parts of the transverse wave

Trough – the “low” parts of the transverse wave

Longitudinal WavesLongitudinal Waves – waves whose mediums move in the same direction as overall wave travel

-- like squeezing and releasing a slinky spring

-- longitudinal waves are often called compressional waves

Parts of a Longitudinal wave

Compressions – areas where the molecules in the medium are tightly squeezed together

Rarefactions – areas where the molecules in the medium are spread apart

Surface WavesSurface Waves – waves that form at the boundary between two different mediums

-- the bouncing of waves vibrating differently create circular-shaped waves

Wave PropertiesDespite the different types of waves, all waves share the same basic properties:

-- amplitude

-- wavelength

-- frequency

-- speed

When figuring out these properties on either longitudinal or transverse waves, it is necessary to remember the following:

Crests on a transverse wave are equal to compressions on a longitudinal wave

Troughs on a transverse wave are equal to rarefactions on a longitudinal wave

AmplitudeAmplitude – the maximum distance the particles of a medium move from their rest position

For a transverse wave:

-- to find amplitude, you measure the height of the crest from the REST POSITION (or the depth of the trough)

For a longitudinal wave:

-- to find amplitude, you measure how strongly compressed the compressions are (or how far apart the rarefactions are spread)

amplitude

WavelengthWavelength – how much of the medium is between corresponding parts of a repeating wave

-- wavelength is measured in meters, and is represented in formulas by the Greek letter lambda (λ)

For a transverse wave:-- you find wavelength by measuring the distance

between crests (or troughs)

For a longitudinal wave:

-- you find wavelength by measuring the distance between compressions (or rarefactions)

wavelength

FrequencyFrequency – the number of complete waves that pass a specific point in a given amount of time (usually 1 second)

-- frequency is measured in a unit called Hertz (Hz), which is equal to waves/second (really is the unit per second)

-- frequency is represented by the Greek letter nu (ν)

To find the frequency of any wave, either count the number of crests or the number of compressions that pass a specific point in a given amount of time, then solve

Period – the amount of time it takes for one complete wave to pass

-- period is the inverse of frequency

Ex: If a wave has a frequency of 3 Hz (3 waves pass per second, then its period is 1/3 second (it takes 1/3 of a second for one wave to pass)

SpeedThe speed of a wave is how much of a medium passes by a specific point in a given amount of time

-- speed is in the units of meters per second (m/s)

The speed of the wave is entirely determined by the medium through which the wave passes.

We can calculated wave speed with the following equation:

Speed = wavelength x frequency

OR

s = λ x ν

Of course: λ = (s / ν) and ν = (s / λ)

vs /

Practice Problems1. An ocean wave passes a buoy 5 times in 20 seconds.

a) What is the frequency of this wave?

b) What is the period of this wave?

c) If the wave has a wavelength of 10 meters, what is the speed of this wave?

More Practice Problems2. The speed of a rope is 40 m/s and its wavelength is 5 m.

a) What is the frequency of this wave?

b) What is the period of this wave?

3. A wave with a period of 0.2 seconds travels at a speed of 60 m/s. What is the wavelength of this wave?