Stationary Waves

Stationary wave

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

Do stationary waves transfer energy

No

How can a stationary wave be demonstrated with a string

1- Attach a vibration transducer at one end of a stretched string, with the other end fixed. The transducer is given a wave frequency by a signal generator and creates a wave by vibrating the string

2- The wave generated by the vibration is reflected back and forth

3- Alter the signal generator to a resonant frequency

Resonant frequency

An exact number of half-wavelength fits onto the string

What does a resonant frequency produce

A stationary wave

What are stationary waves also called

Standing waves

What are stationary waves made up of

Nodes and antinodes

Node

Zero displacement due to destructive interference

Antinode

Maximum displacement due to constructive interference

How long is 1 wavelength of a stationary wave

2 node-nodes

How long is ½ a wavelength of a stationary wave

1 node-node

Name the first 3 harmonics

-Fundamental mode of vibration

-Second harmonic

-Third harmonic

What is the lowest possible resonant frequency

The fundamental mode of vibration

How many wavelengths is the fundamental mode of vibration

½

How many wavelengths is the second harmonic

1

How many wavelengths is the third harmonic

1½

Ways to demonstrate stationary waves

-Reflected microwaves

-Powder

Explain how stationary waves are demonstrated using reflected microwaves

A microwave transmitter transmits microwaves which reflect off a metal plate and are picked up by a moveable probe, connected to a meter. The reading will be strongest at antinodes and 0 at nodes

Explain how stationary waves are demonstrated by powder

Lycopodium powder is in a closed glass tube, with a loudspeaker at one end. The powder is shaken away at antinodes, but is undisturbed at nodes

μ symbol

Mass per unit length

Experiment to investigate factors affecting resonant frequencies of a string

1- Fix a string to a vibration transducer attached to a signal generator on a bench. Attach the string to a pulley and some masses over the edge of the bench.

2- Calculate μ with the mass of the string/length of the string

3- Calculate the with mass of the weights x g

4- Turn on the signal generator and vary the frequency until you find the first harmonic

5- Alter length, tension or μ

How to do the stationary wave experiment with altered length

Move the vibration transducer towards or away from the pulley, find the first harmonic and record f against length

How to do the stationary wave experiment with altered tension

Add or remove masses, find the first harmonic and record f against T

How to do the stationary wave experiment with altered μ

Use different string samples, find the first harmonic and record f against μ

Speed of a transverse wave on a string equation

v = root(T/μ)

How does increasing the length of the string affect resonant frequency

Decreases it

How does increasing μ of the string affect resonant frequency

Decreases it

How does having a looser string affect resonant frequency

Decreases it

Amplitude distribution of a stationary wave vs progressive wave

Amplitude varies in a stationary wave, whilst it is the same at all points of a progressive wave