General Properties of Waves Notes

Cambridge IGCSE Physics: Revision notes

Key facts

Waves transfer energy without transferring matter.
Wave speed $v = f\lambda$ ; frequency and period are linked by $f = \dfrac{1}{T}$ .
Transverse waves vibrate at right angles to travel; longitudinal waves vibrate parallel to it.
When a wave changes medium, its frequency stays the same; speed and wavelength change together.
Reflection, refraction and diffraction are the three wave behaviours; more diffraction when the gap is close to the wavelength.

Waves carry energy

A wave carries energy from place to place. The particles only vibrate about their rest position and are not carried along.

Each particle passes energy to the next, so the wave travels while the particles stay put. Water rises and falls, air particles vibrate, and electromagnetic waves cross a vacuum with no medium at all.

A wavetransfers energy, not matter

A cork floats on a water wave. What does it do as the wave passes?

Describing a wave

Amplitude, wavelength, frequency and period describe any wave, and frequency is one over period.

Amplitude is the maximum displacement from the rest position. Wavelength is the distance between consecutive crests. Frequency is the number of waves passing a point per second, in hertz (Hz). Period is the time for one wave.

Wavefronts join points that are in phase.

A transverse wave: crests, troughs and amplitude

Frequency $f = \dfrac{1}{T}$

Worked example

A wave has a wavelength of 0.5 m and 10 waves pass a point each second. Find the frequency and the period.

1
10 waves pass per second, so $f = 10$ Hz.
2
$T = 1 \div f = 1 \div 10 = 0.1$ s.

A wave has period 0.02 s. What is its frequency?

The wave equation

Wave speed equals frequency multiplied by wavelength.

Units: speed in m/s, frequency in Hz, wavelength in m. Rearrange to $f = v \div \lambda$ or $\lambda = v \div f$ .

In one medium the speed is fixed, so doubling the frequency halves the wavelength. Use the sliders to see how amplitude and wavelength change the picture.

Wave speed $v = f\lambda$

a = 1amplitudew = 4wavelength (m)

Change the amplitude and the wavelength of a wave

Worked example

A sound wave travels at 330 m/s with a frequency of 440 Hz. Find its wavelength.

1
Rearrange: $\lambda = v \div f$ .
2
$\lambda = 330 \div 440 = 0.75$ m.

A wave changing medium

A water wave has speed 2 m/s and frequency 4 Hz. It then moves into shallower water, where its speed drops to 1.5 m/s. Find the wavelength before and after.

1
Before: $\lambda = 2 \div 4 = 0.5$ m.
2
The frequency stays at 4 Hz.
3
After: $\lambda = 1.5 \div 4 = 0.375$ m.

A wave of frequency 5 Hz has wavelength 2 m. What is its speed?

Transverse and longitudinal

Transverse waves vibrate at right angles to the direction of travel; longitudinal waves vibrate parallel to it.

Transverse waves have crests and troughs. Longitudinal waves have compressions (high pressure) and rarefactions (low pressure) and cannot travel through a vacuum. Electromagnetic waves are transverse and do not need a medium.

Transverse

Vibration perpendicular to travel
Crests and troughs
Light, water waves, S-waves

Longitudinal

Vibration parallel to travel
Compressions and rarefactions
Sound, P-waves

Which wave needs a medium to travel?

Reflection, refraction, diffraction

Waves reflect off barriers, refract when their speed changes and diffract through gaps and around edges.

Reflection: the wave bounces back with angle of incidence equal to angle of reflection.

Refraction: the wave changes speed in a new medium. It bends towards the normal if it slows down and away if it speeds up.

Diffraction: the wave spreads out through a gap or round an edge. Longer wavelength and narrower gap give more spreading.

ReflectionRefractionDiffractionSpeedSameChangesSameWavelengthSameChangesSameFrequencySameSameSameWhat happensDirection changes, i = rWave bendsWave spreads out

	Reflection	Refraction	Diffraction
Speed	Same	Changes	Same
Wavelength	Same	Changes	Same
Frequency	Same	Same	Same
What happens	Direction changes, i = r	Wave bends	Wave spreads out

Reflection

Speed:: Same
Wavelength:: Same
Frequency:: Same
What happens:: Direction changes, i = r

Refraction

Speed:: Changes
Wavelength:: Changes
Frequency:: Same
What happens:: Wave bends

Diffraction

Speed:: Same
Wavelength:: Same
Frequency:: Same
What happens:: Wave spreads out

Worked example

Sound of frequency 1000 Hz and wavelength 0.34 m travels at 340 m/s in air. It enters water, where sound travels at 1500 m/s. Find the new wavelength.

1
The frequency stays at 1000 Hz.
2
$\lambda = v \div f = 1500 \div 1000 = 1.5$ m.

A wave slows down on entering shallow water. What happens to its wavelength?

The ripple tank

A ripple tank shows reflection, refraction and diffraction of water waves as shadows on a screen.

A light above a shallow tank casts the shadow of the wavefronts onto a screen below. Change the wavelength by changing the dipper frequency: short wavelengths diffract less, long wavelengths diffract more.

Reflection

Flat barrier
Angle in = angle out

Refraction

Shallow region (submerged glass sheet)
Waves slow, wavelength falls, bend towards normal

Diffraction at a gap

Barriers with a gap
Narrower gap, more spreading

Diffraction at an edge

One straight barrier
Waves bend into the shadow

Worked example

In a ripple tank, a wave of wavelength 4 cm moves into shallower water, where it slows to half its original speed. Find the new wavelength.

1
The frequency stays constant.
2
$\lambda = v \div f$ , so halving $v$ halves $\lambda$ .
3
New wavelength $= 4 \div 2 = 2$ cm.

In a ripple tank the gap is made narrower. What happens to the diffraction?

Try an exam question

A sound wave has frequency 440 Hz and speed 330 m/s in air. Calculate its wavelength, and state what happens to the frequency when it enters water.

[4 marks]

That's the notes covered.

Carry on to the next subtopic.