Waves Basics

Basic Waves

Define a wave.

A means of transferring energy via oscillations without any net transfer of matter.

What does a wave transfer?

Energy.

Do waves cause a net movement of matter?

No, particles oscillate about their equilibrium positions but there is no net transfer of matter.

Define an oscillation.

A repeated motion or variation about an equilibrium position.

What is a mechanical wave?

A wave that requires a material medium through which to travel.

Why do mechanical waves require a medium?

Particles in the medium oscillate and transfer energy from one particle to another.

Give an example of a mechanical wave.

A sound wave.

How does a sound wave transfer energy?

Through repeated vibrations of particles in a material medium.

What is an electromagnetic wave?

A wave consisting of oscillating electric and magnetic fields.

Do electromagnetic waves require a material medium?

No, they can travel through a vacuum.

How do electromagnetic waves transfer energy?

Through oscillations of electric and magnetic fields.

Give an example of an electromagnetic wave.

Light.

Define displacement.

The position of a point on a wave at a particular instant relative to its equilibrium position.

What symbol is commonly used for displacement?

x.

What is the SI unit of displacement?

Metre (m).

What is the equilibrium position?

The position about which a particle or point oscillates.

Define amplitude.

The magnitude of the maximum displacement from the equilibrium position.

What symbol is used for amplitude?

A.

What is the SI unit of amplitude?

Metre (m).

How is amplitude found from a displacement graph?

Measure from the equilibrium position to a crest or trough.

Is amplitude the distance from a crest to a trough?

No. The crest-to-trough distance is twice the amplitude.

Define a crest.

The point of maximum positive displacement on a wave.

Define a trough.

The point of maximum negative displacement on a wave.

Define frequency.

The number of complete wave cycles or oscillations per second.

What symbol is used for frequency?

f.

What is the SI unit of frequency?

Hertz (Hz).

What does 1 Hz mean?

One complete oscillation or wave cycle per second.

Define wavelength.

The distance between a point on a wave and the equivalent point on the next cycle.

What symbol is used for wavelength?

λ.

What is the SI unit of wavelength?

Metre (m).

How can wavelength be measured on a wave graph?

Measure the distance between two adjacent points in phase, such as crest to crest or trough to trough.

Define period.

The time taken for one complete oscillation at a point on a wave.

What symbol is used for period?

T.

What is the SI unit of period?

Second (s).

State the relationship between frequency and period.

f = 1/T.

State the equation for period in terms of frequency.

T = 1/f.

What happens to the period when frequency increases?

The period decreases.

What happens to frequency when the period increases?

The frequency decreases.

Define phase.

The stage that a point on a wave has reached within a complete cycle.

How can phase be measured?

In radians or degrees.

How many radians are in one complete wave cycle?

2π radians.

How many degrees are in one complete wave cycle?

360°.

What does it mean for two points to be in phase?

They are at the same stage of their oscillation and moving in the same direction.

What is the phase difference between points one wavelength apart?

2π radians or 360°.

What is the phase difference between points half a wavelength apart?

π radians or 180°.

Define wave speed.

The rate at which the wave travels.

What symbol is normally used for wave speed?

v.

What symbol may be used for the speed of electromagnetic waves?

c.

What is the SI unit of wave speed?

m s⁻¹.

State the wave equation.

v = fλ.

What does v represent in v = fλ?

Wave speed in m s⁻¹.

What does f represent in v = fλ?

Frequency in Hz.

What does λ represent in v = fλ?

Wavelength in metres.

How can frequency be calculated using wave speed and wavelength?

f = v/λ.

How can wavelength be calculated using wave speed and frequency?

λ = v/f.

Why does v = fλ give wave speed?

In one period a wave travels one wavelength, so speed = wavelength ÷ period = λ/T = fλ.

What does a displacement–distance graph show?

The displacement of different points on a wave at one instant in time.

What can be determined from a displacement–distance graph?

Amplitude and wavelength.

What does a displacement–time graph show?

How the displacement of one point on a wave changes with time.

What can be determined from a displacement–time graph?

Amplitude and period.

Can wavelength be measured directly from a displacement–time graph?

No, because its horizontal axis represents time rather than distance.

Can period be measured directly from a displacement–distance graph?

No, because its horizontal axis represents distance rather than time.

How is wave speed related to distance and time?

v = distance/time.

How can the speed of sound in air be investigated using two microphones?

Place two microphones at different distances from a loudspeaker, display their signals on a twin-beam oscilloscope and use the time delay and microphone separation to calculate speed.

How can wave speed be calculated from microphone separation and time delay?

v = d/t.

What is a twin-beam oscilloscope?

An oscilloscope with two inputs that displays both signals so they can be compared.

How can wavelength be measured using two microphones and an oscilloscope?

Move one microphone until the two traces return to the same phase; the distance moved between successive in-phase positions is one wavelength.

How can the speed of sound be calculated after finding wavelength experimentally?

Use v = fλ, where the frequency is set by the signal generator.

Why should oscilloscope traces be synchronised when measuring sound speed?

To reduce random uncertainty when comparing the positions of the traces.

What does it mean when two oscilloscope traces are in phase?

Their corresponding peaks, troughs and other points occur at the same phase positions.

What is a pulse-echo technique?

A method in which a wave pulse is emitted, reflected from an object and detected when it returns.

What happens to a pulse when it reaches a reflecting object?

It is reflected back towards the detector as an echo.

How can pulse-echo techniques be used to determine distance?

Measure the time between sending the pulse and receiving its echo, then use the wave speed to calculate the distance.

Why must the calculated pulse-echo distance usually be divided by two?

The measured time includes the journey to the object and back again.

State the equation for distance to an object using pulse-echo measurements.

d = vt/2.

What does t represent in d = vt/2?

The total time taken for the pulse to travel to the object and return.

What does v represent in d = vt/2?

The speed of the wave.

Why is there a factor of 1/2 in d = vt/2?

The pulse travels twice the distance between the source and the object.

What is echolocation?

The use of emitted sound pulses and their echoes to determine the position or properties of objects.

How do bats use echolocation?

They emit high-frequency sound pulses and use the returning echoes to determine the locations of nearby objects.

What type of sound do bats use for echolocation?

Ultrasound.

Approximately what frequencies can bats use for echolocation?

About 50–100 kHz.

How do dolphins use pulse-echo techniques?

They emit sound and analyse returning echoes to locate and identify objects underwater.

Give technological applications of pulse-echo techniques.

Radar, sonar, medical imaging and distance measurement.

How does radar use pulse-echo measurements?

Radio waves are emitted and their reflected pulses are detected to determine the distance to an object.

How does sonar use pulse-echo measurements?

Sound waves are emitted underwater and their echoes are used to determine distances or locate objects.

Why are pulse-echo techniques useful when direct measurement is difficult or dangerous?

They allow distances and objects to be investigated remotely.

What speed should be used in a pulse-echo calculation?

The speed of the particular wave in the medium through which it is travelling.