15 Waves
speed of light in a vacuum c = 3.0 × 108 m s−1
speed of sound in air = 340 m s−1
Intermediate level
1
For a progressive wave, define the following terms:
a
b
c
2
[1]
[1]
[1]
Calculate the frequency of the following waves:
a
b
3
amplitude
wavelength
frequency.
red light of wavelength 6.5 × 10–7 m emitted from a light-emitting diode
ultrasound of wavelength 7.0 mm emitted by a bat.
[2]
[2]
In a water tank, a dipper oscillating at a frequency of 30 Hz produces surface water waves of
wavelength 2.5 cm.
a
b
Calculate the speed of the water waves.
Determine the wavelength of the waves when the frequency of the dipper is doubled.
[2]
[2]
Higher level
4
Displacement against time graphs for two waves A and B of the same frequency are
shown below.
Determine the period and the frequency of the waves.
5
[2]
An oscilloscope has its time base and Y sensitivity (Y gain) set on 0.5 ms cm−1 and 0.5 V cm−1
respectively. A person whistles into a microphone connected to the oscilloscope. The trace
displayed on the oscilloscope screen is shown below.
a
Determine the frequency of the sound wave.
[2]
b Calculate the wavelength of the sound
produced by the whistle.
c Describe how the oscilloscope trace would
change for a louder whistle of half the
frequency of a.
[2]
[2
6
You can use the following equation to determine the intensity of a wave:
power
cross - sectional area
This equation can be applied to all waves, including sound.
intensity 
The intensity of sound at a certain distance from a loudspeaker is 3.5 × 10−3 W m−2.
The amplitude of the sound waves at this point is known to be 0.45 mm. Calculate:
the power transmitted through a cross-sectional area of 8.0 × 10−5 m2 when the intensity
of sound is 3.5 × 10−3 W m–2
b the intensity of sound where the amplitude is 0.90 mm
c the amplitude of the sound waves where the intensity is 5.6 × 10−2 W m−2.
a
[2]
[3]
[3]
Extension
7
The intensity of a wave may be defined as the power transmitted per unit cross-sectional
area at right angles to the direction of travel.
a
For a point source of light, explain why the intensity I at a distance r away from the source
obeys an inverse square law with distance, that is:
1
[3]
I 2.
r
b The intensity of visible light from the Sun reaching the upper parts of our atmosphere is
about 1.4 kW m−2. The Sun has a radius of 7.0 × 108 m and is 1.5 × 1011 m from the Earth.
Calculate:
i the intensity of visible light emitted from the Sun’s surface
[3]
ii the total power radiated by the Sun in the visible region of the electromagnetic spectrum [2]
iii the intensity of light from the Sun at the planet Neptune. (Neptune is 4.5 × 1012 m from
the Sun.)
[3]
Total:
38
Score:
%
16 Electromagenetic waves
speed of light in a vacuum c = 3.0 × 108 m s−1
Intermediate level
1 a State two common properties of all the waves in the electromagnetic spectrum.
b State one main difference between X-rays and sound waves.
2
Complete the table below, naming the electromagnetic radiation with each specified
wavelength.
[3]
Wavelength/m
2 × 10−10
4.5 × 10−2
[2]
[1]
2.5 × 103
Name of radiation
3
A television remote control emits infrared radiation of wavelength 8.5 × 10−7 m. Calculate:
a the frequency of this infrared radiation
b the distance travelled by the infrared radiation in a time of 0.20 s.
[2]
[2]
4 Explain what is meant by plane polarised light.
[1]
5
Visible light and microwaves can be polarised. What can be deduced about the nature of
these two waves?
[1]
6
Two types of ultraviolet radiation reaching the Earth’s surface are UV-A and UV-B.
a What does UV-A do to our skin?
b State one advantage and one disadvantage of exposure to UV-B.
[1]
[2]
Higher level
7 a Give typical values for the wavelength of X-rays and of -rays.
[2]
b Use your values in a to determine the ratio:
frequency of  - rays
ratio =
[2]
frequency of X - rays
8
Astronomers detect intense electromagnetic radiation of frequency 300 GHz coming from all
directions of the sky as evidence of the Big Bang. Determine the wavelength of this radiation,
and hence name the region of the electromagnetic spectrum where this radiation may be
detected.
[3]
9
Describe how you can show that reflected light from a shiny surface such as glass is (partially)
polarised.
[2]
10 a State Malus’s law.
[1]
b Vertically polarised light is incident on a polaroid whose axis is at 30° to the vertical.
The incident intensity of light is 0.48 W m−2. Calculate the intensity of the transmitted light
through the polaroid.
[3]
Extension
11
Our modern society relies heavily on communication using radio waves. Radio waves
generated by a transmitter have to propagate through the atmosphere, and sometimes empty space,
in order to reach the receiver. Depending on their frequency, there are three modes (methods) by
which they reach their destination: as surface waves, sky waves or space waves.
Use the internet to find the frequencies and some of the characteristics of these waves.
Total:
28
Score:
%
17 Superposition of waves
speed of light in a vacuum c = 3.0 × 108 m s−1
Intermediate level
1
State the principle of superposition of waves.
[1]
2 a Describe what is meant by the diffraction of a wave.
b Electromagnetic radiation of frequency 7.5 × 109 Hz is directed towards a slit
of width 6.0 cm.
i Determine the wavelength of the radiation.
ii Explain whether or not the radiation will be diffracted at the slit.
3
Explain what is meant by coherent sources.
[1]
4
[1]
[2]
[1]
The diagram below shows the displacement against time graphs for two waves A and B.
a What is the phase difference between the two waves?
[1]
b The two waves A and B are combined. Name the type of interference that will occur.
[1]
5The diagram below shows an arrangement used to demonstrate the interference of water waves.
a
Constructive interference occurs at point A. What is the path difference of the waves from
the gaps S1 and S2?
[1]
b The water waves have a wavelength of 3.0 cm. Determine the path difference for
the waves arriving at point B. Name the type of interference taking place at this point.
[3]
6
A two-slit arrangement is used to determine the wavelength  of light. The wavelength is
given by the equation:
ax
D
Define the terms in the equation above.
=
[3]
Higher level
7
A microwave source is directed towards a metal plate with two narrow vertical slits. A
receiver is slowly moved along the line XY as shown in the diagram.
a Explain why the receiver registers a series of maxima and minima.
b The wavelength of the microwaves is 2.8 cm. The separation between the slits is 4.0 cm
and the receiver is a distance of 80 cm from the slits. Calculate the separation between
adjacent maxima.
c Describe the effect on your answer to b when:
i the separation between the slits is halved
ii the distance between the slits and the receiver is doubled.
8
Monochromatic light is incident normally at a diffraction grating with 60 lines per mm.
The tenth-order maximum is observed at an angle of 19°. Determine:
[3]
[3]
[1]
[1]
a the spacing (in metres) between the centres of the adjacent lines
[2]
b the wavelength of incident light.
[3]
9
Yellow light of wavelength 5.5 × 10−7 m is incident normally at a diffraction grating with
300 lines per mm. Calculate the angle between the first-order and second-order maxima.
[5]
10
Blue light of wavelength 4.5 × 10−7 m is incident normally at a diffraction grating with
100 lines per mm. Calculate the maximum number of orders that can be observed.
[4]
Extension
11
Answer the following questions with supporting calculations.
You are given a diffraction grating with 40 lines per mm.
The diffraction grating is mounted on an instrument that can measure angles to within 0.1°.
Can this instrument be used to determine the individual wavelengths of spectral lines of
wavelengths 589.6 nm and 589.0 nm?
[6]
b White light is incident normally at the grating. Estimate the angle between the extreme
ends of the spectrum for the tenth-order maxima.
[4]
a
Total:
47
Score:
%