Formation of a standing wave by
reflection
• A travelling wave is reflected
• The reflected wave is 180° out of phase with
the original wave
• The two waves travelling in opposite
directions superimpose and interfere
• A standing wave is produced with nodes at
points of destructive interference and
antinodes at points of constructive
interference
Travelling waves and standing waves
• Travelling waves transfer energy, standing
waves do not.
• All points on a travelling wave have the same
amplitude, in a standing wave they do not.
• On either side of a node, the points on a
standing wave are 180° out of phase.
Standing Waves on a String
On a stretched string
Creating Standing Waves
• Slowly increase the frequency from 10 Hz to X Hz.
• You should first see a standing wave with a single
'hump'.
• As the frequency is increased a wave with two
'humps' will appear, then three and so on.
• The 'humps' are 'antinodes' and the points of
least movement are 'nodes'.
• The nodes are half a wavelength apart.
• These standing waves can be clearly seen using
the stroboscope to 'freeze' the movement.
Creating standing waves 2
• Make a note of the frequency of the signal
generator each time a standing wave is
produced.
• Q - What is the relationship between the
wavelength of the standing wave and the
frequency of vibration?
• Q - Why do you think that standing waves are
only observed for specific frequencies?
In a closed tube
In an open tube
Stationary (Standing) waves
When two identical waves travelling in opposite directions, cross each other,
they interfere with each other to produce a wave shape that stands still on the
spring. The product wave is called a stationary wave.
A stationary wave can either result from an interference between two
identical waves travelling in opposite direction or a wave interfering with
its reflection.
http://www.walter-fendt.de/ph14e/stwaverefl.htm
Stationary (Standing) waves
When two identical waves travelling in opposite directions, cross each other,
they interfere with each other to produce a wave shape that stands still. The
product wave is called a stationary wave.
A stationary wave can either result from an interference between two
identical waves travelling in opposite direction or a wave interfering with
its reflection.
http://www.walter-fendt.de/ph14e/stwaverefl.htm
Waves on a tensioned rubber cord
Tension a rubber cord and anchor its ends.
Set the cord to vibrate at 1 Hz
Increase the vibrating frequency gradually until you observe a stationary wave.
Measure the distance between the nodes
record the frequency and the wavelength
Repeat the procedure with different frequencies to find the first five stationary wave patterns.
Use your results to find the speed on the rubber cord.
Shape of cord
Frequency Distance between
two consecutive
/Hz
nodes/m
Wavelength
/m
Speed
/ms-1
S ig n a l g e n e ra to r
F re q ue nc y A dju st
5
3
7
8
2
1
1 0H z
1 00 H z
1k H z
10 k H z
9
1 00 kH z
F req ue nc y ran g e
1 000
1 00
10
1
1000
10
h a rd b o a rd
(p a rtia l re fle cto r)
10 0
Fre qu en cy
W av e
55 H z
O u tpu ts
A
p ow er
Sp e a k e r
1 .5 m
m icro p h o n e
m s/d iv
5
10
2
50
0 .5
1
20
X -s h ift
V /d iv
5
10
2
50
0 .5
1
20
Y-s h ift
in pu ts
fo c us
A
brigh tne ss
o s cillo s c o p e
B
C
D
1. Set the signal generator to give a note of around 3000 Hz
from the loudspeaker.
2. Place the reflector about 1.5 m from the loudspeaker.
3. Place the microphone in between the loudspeaker and
reflector – pointing at the loudspeaker.
4. Move the microphone slowly towards the reflector. You will
observe places of maximum and minimum signal.
5. Place the microphone at a position of minimum signal and
remove the reflector so that less sound is reflected back. How
the signal at the microphone increase, if less sound can is
now reaching it?
6. The distance between two points of minimum signal is half
a wavelength. Measure and record the distance moved by the
microphone between a number of points of minimum signal,
and calculate the wavelength.
7. Your value for the wavelength can be checked using
v = f λ and taking the velocity of sound in air to be 340 m s–1.
m icro w a ve tra n sm itte r
d io d e re ce ive r
re fle cto r
1. Place the reflector about 1.5 m from the transmitter.
2. Place the diode probe between the transmitter and the reflector.
3. Slowly move the probe along the line between transmitter and reflector.
4. Note what happens to the strength of the received signal as the probe moves towards the
transmitter.
5. Measure the average distance between pairs of minima (two nodes).
6. Use this to find the wavelength of the radiation.
Quiz
Which of the following describes the type of wave produced on a
stretched guitar string after it has been plucked?
a.
b.
c.
d.
Progressive, longitudinal, electromagnetic
Progressive, transverse, mechanical
Stationary, longitudinal, electromagnetic
Stationary, transverse, mechanical
Which of the following phenomena cannot be demonstrated using
sound waves?
a.
b.
c.
d.
Diffraction
Polarisation
Reflection
Superposition
When a two slit arrangement was set up to produce a superposition pattern on a screen
using a monochromatic source of green light, the fringes were found to be too close
together for accurate observation. It would be possible to increase the separation of
the fringes by:
a.
b.
c.
d.
Replacing the light source with a monochromatic source of red light
Increasing the distance between the source and the slits
Decreasing the distance between the slits and the screen
Increasing the distance between the two slits
Two waves of equal amplitude and frequency are travelling in opposite directions along
the same path with speeds of 75ms-1 . Their frequency is 50Hz. The distance
between adjacent nodes of the resulting stationary wave is
a.
b.
c.
d.
0.33 m
0.67 m
0.75 m
1.5 m
True or false?
Progressive waves can be polarised whereas stationary waves cannot be
polarised.
false
True or false?
Amplitude is either constant or gradually declines along a progressive wave
whereas amplitude depends on the position along a stationary wave.
True
True or false?
Energy is continually transferred along a progressive wave whereas there is no
transfer of energy along a stationary wave.
True
A taut wire is fixed at one end whilst the other end is attached to a small vibration
generator. The wire is set vibrating so that there are nodes at both ends and a
single node along the wire at its centre.
True or false?
All points of the wire on one side of the centre vibrate in phase with each other.
True
A taut wire is fixed at one end whilst the other end is attached to a small vibration
generator. The wire is set vibrating so that there are nodes at both ends and a
single node along the wire at its centre.
True or false?
The wavelength of the waves on the wire equals the length of the wire
True
A taut wire is fixed at one end whilst the other end is attached to a small vibration
generator. The wire is set vibrating so that there are nodes at both ends and a
single node along the wire at its centre.
True or false?
Two points on the wire at equal distances from the centre have the same amplitude
True
A taut wire is fixed at one end whilst the other end is attached to a small vibration
generator. The wire is set vibrating so that there are nodes at both ends and a
single node along the wire at its centre.
True or false?
Any two points on either side of the centre vibrate with a phase difference of 90°
False , the phase difference is 180 °
w
1.2mm
w
1.2mm
This pattern was obtained on a screen with green light and a double slit
1m away from the screen. Green light has a wavelength of 500nm.
What is the slit separation?
w = λD/s
s = λD/w
s = 500x10-9x1/1.2x10-3
s= 4.16x10-4m (0.4mm)
w
w
red
blue
If white light is used instead of green monochromatic light, a less clear
interference pattern is produced.
The central fringe is white because every colour contributes at the centre of the pattern.
The next fringe is tinged with blue on the inner side and red on the outer side. Red light
has a longer wavelength, so it produces wider fringes
The intensity decreases the further the distance from the centre