3.5 Stationary Waves

Question 1

What is a stationary wave?

Answer 1

The superposition of two progressive waves with the same frequency and amplitude moving in opposite directions

Question 2

What is the difference between stationary waves and progressive waves?

Answer 2

No energy is transferred by stationary waves, unlike progressive waves

Question 3

How can you demonstrate stationary waves?

Answer 3

• set up a driving oscillator at one end of a stretched string with the other end fixed
• the wave generated by the oscillator is reflected back and forth
• at certain frequencies (resonant frequencies) the oscillator produces an exact number of waves for the waves to reinforce each other
• this causes a stationary wave where the overall pattern doesn’t move
• the stationary waves are transverse

Question 4

What is a node on a stationary waves?

Answer 4

Points on the wave where the amplitude of the vibration is zero

Question 5

What is an antinode on a stationary waves?

Answer 5

Points of maximum amplitude

Question 6

What is the interference at a node?

Answer 6

At a node there is total destructive interference - the displacement of the two waves always cancel each other out

Question 7

What is the interference at an antinode?

Answer 7

There is constructive interference - the displacements of the two waves combine to make a bigger displacement

Question 8

What is a resonant frequency?

Answer 8

The only frequencies where a stationary wave can be formed
This is when an exact number of half wavelengths fits on the string

Question 9

What is the first harmonic?

Answer 9

The lowest possible resonant frequency
It has one ‘loop’ with a node at each end
One half wavelengths fits onto the string, and so the wavelength is double the length of the string

Question 10

What is the second harmonic?

Answer 10

Twice the frequency of the first harmonic
It has two ‘loop’ with nodes in the middle and at each end
Two half wavelengths fit onto the string, and so the wavelength is the length of the string

Question 11

How many harmonics can you have?

Answer 11

As many as you like
An extra loop and an extra node is added with each one
The wavelength increases by 1/2 the length of the string and the frequency increases by the value of the frequency of the first harmonic

Question 12

How can you demonstrate stationary waves using microwaves?

Answer 12

• reflect a microwave beam at a metal place
• the superposition of the wave and its reflection produces a stationary wave
• you can find the nodes and the antinodes by moving the probe between the transmitter and reflecting plate
• the meter/loudspeaker receives no signal at the nodes and maximum signal at the antinodes

Question 13

How can you demonstrate stationary waves using stationary sound waves?

Answer 13

• powder in a tube of air can show stationary sound waves
• a loudspeaker produces stationary sound waves in the glass tube
• the power laid along the bottom of the tube is shaken away from the antinodes but left undisturbed at the nodes
• the distance (d) between each node is lambda/2 so the speed can be found by measuring d and knowing the frequency of the signal generator