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

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

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.

Stationary (Standing) waves

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

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.

Waves on a tensioned rubber cord

Shape of cord Frequency/Hz

Distance between two consecutive nodes/m

Wavelength/m

Speed/ms-1

Tension a rubber cord and anchor its ends.Set the cord to vibrate at 1 HzIncrease the vibrating frequency gradually until you observe a stationary wave.Measure the distance between the nodesrecord the frequency and the wavelengthRepeat the procedure with different frequencies to find the first five stationary wave patterns.Use your results to find the speed on the rubber cord.

1

2

3

5

7

8

9

Frequency Adjust

1

10

1001000

10

100

1000

Frequency range

Outputs

A

power

10Hz 100kHz1kHz 10kHz100Hz

Frequency

55 HzWave

Signal generator

Speaker

focus

brightness

50

20

10

5

2

1

0.5

ms/div

X-shift

50

20

10

5

2

1

0.5

V/div

Y-shift

inputs

A B C D

microphone

oscilloscope

1.5 m

hardboard(partial reflector)

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.

microwave transmitterdiode receiver

reflector

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. Progressive, longitudinal, electromagneticb. Progressive, transverse, mechanicalc. Stationary, longitudinal, electromagneticd. Stationary, transverse, mechanical

Which of the following phenomena cannot be demonstrated using sound waves?

a. Diffraction b. Polarisationc. Reflectiond. 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. Replacing the light source with a monochromatic source of red lightb. Increasing the distance between the source and the slitsc. Decreasing the distance between the slits and the screend. 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. 0.33 mb. 0.67 mc. 0.75 md. 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 w

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?

1.2mm 1.2mm

w = λD/s

s = λD/w

s = 500x10-9x1/1.2x10-3 s= 4.16x10-4m (0.4mm)

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 fringesThe intensity decreases the further the distance from the centre

wblue

wred