AH 3.3.1 Waves Properties 3.3.2 Travelling Waves 3.3.3 Stationary Waves

Question 1

Copy and complete:

In wave motion ………………….. is transferred with no net ………………. transport.

Answer 1

In wave motion energy is transferred with no net mass transport.

Question 2

Copy and complete:

The intensity of a wave is ………………………….. proportional to its ………………………. squared.

This may be expressed by the equation ………………………….

where k = constant

A = amplitude of wave

Answer 2

In wave motion energy is transferred with no net mass transport.

This may be expressed by the equation

Intensity = kA²

where k = constant

A = amplitude of wave

Question 3

The simplest mathematical form of a wave uses which mathematical functions?

Answer 3

Sine and cosine

Question 4

All waveforms can be described by the superposition of what?

Answer 4

Sine or cosine waves.

Question 5

The equation of a travelling wave is given by

y = a sin 2π (ft – x/λ)

State what the following terms mean and give their units.

y, a, f ,t, x, λ

Answer 5

y = the transverse displacement of the wave medium (or the energy of an EM wave's field)
a = the amplitude of the wave (= the medium’s maximum transverse displacement)
f= frequency of the wave
t = time elapsed since wave has left source
x = the distance travelled by a wave front form source
λ = the wavelength of the wave

Question 6

In the equation of a travelling wave

y = a sin 2π (ft – x/λ)

which term represents

a) the periodic disturbance of the wave medium over time?
b) the distance travelled by the wave front perpendicular to the periodic disturbance?

Answer 6

a) 2πft represents the periodic disturbance of the wave medium over time
b) 2πx/λ the distance travelled by the wave front perpendicular to the periodic disturbance

Question 7

Look at the travelling wave shown in the diagram.

a) What is the separation distance of points A & B?
b) What is the wave number, k?
c) What is the phase difference δ in radians, between these two points?

Answer 7

a) By inspection, A & B are separated by 2 m
b) k = θ/x = the no. of radians per metre

= (π/2)/1 …by observing how many radians there are in 1 m

So k = π/2 radians per metre

c) δ = kx = (π/2) x 2

δ = π radians

Question 8

Look at the travelling wave shown in the diagram.

a) What is the separation distance of points A & B?
b) Calculate the wave number, k.
c) What is the phase difference δ between these two points?
d) In general any two points on this wave are separated by a phase angle

ϕ = 2πx/ λ

Use this equation with the diagram to confirm the wavelength of the wave is 8m

Answer 8

a) 6m

b) k = θ/x
= 3π/2 / 6
k = π/4 rad m-1

c) δ = k x
= (π/4) x 6
δ =3π/2

d) ϕ = 2πx/ λ

λ= 2πx/ ϕ

= 2π x 8 / 2π …choosing two points one wavelength apart

λ = 8 m

Question 9

By drawing a labelled diagram, explain in detail what is meant by a stationary wave, basing your answer on a real-life example. Include reference to nodes and antinodes and their spacing.

Answer 9

The diagram below shows a stationery wave on a stretched string.

The string is vibrated at one end by the piston.

The incident wave (shown in red) travels from the piston to the fixed end where it reflects with a π phase change.

The reflected wave (shown in blue) interferes with the incident wave.

The resultantwave produced consists of a series of maxima (antinodes) and minima (nodes). The string is stationary at the nodes. The nodes areλ/2 apart.

Question 10

a) Draw a diagram of a resonating air column in a tube showing the first four harmonics that result.
b) What pattern describes the harmonics?
c) Suggest a musical instrument in which this resonance effect takes place

Answer 10

a) See diagram below
b) The first harmonic (or fundamental note) consists of 1 x λ/2

The second harmonic consists of 2 x λ/2

The third harmonic consists of 3 x λ/2

The fourth harmonic consists of 4 x λ/2

The n^th harmonic consists of n x λ/2

c) E.g. a clarinet or other woodwind or brass instrument.