STATIONARY WAVES
A stationary wave is the superposition of two progressive waves with the same frequency
(wavelength), moving in opposite directions
- no energy is transmitted by a stationary wave
- You can demonstrate stationary waves by setting up a driving oscillator at one end of a
stretched string with the other end xed the wave generated by the oscillator is re ected back
and forth
- For most frequencies the resultant pattern is a jumble. However, if the oscillator happens to
produce an exact number of waves in the time it takes for a wave to get to the end and back
again, then the original and re ected waves reinforce each other.
- At these “resonant frequencies” you get a stationary wave where the pattern doesn’t move
Stationary waves in strings form oscillating loops separated by nodes:
Nodes are where the amplitude of the vibration is zero.
Antinodes are points of maximum amplitude .
An exact number of half wavelengths ts onto the string:
- First Harmonic: this stationary wave is vibrating at the lowest possible resonant frequency. It
has one loop with a node at each end.
- Second Harmonic: it is twice the frequency of the rst harmonic. There are two loops with a
node in the middle and one at each end
- Third Harmonic: is three times the frequency of the rst harmonic. 1 1/2 wavelengths t on the
string
Between two nodes every part of the wave is in phase, across a node the parts of the wave are
180 degree out of phase
You can demonstrate stationary waves with microwaves and sounds:
- microwaves re ected o a metal plate set up a stationary wave: microwave stationary wave
apparatus. You can nd the nodes and antinodes by moving the probe between the transmitter
and re ecting plate
- powder can show stationary waves In a tube of air: stationary sound waves are produced in the
glass tube. The lycopodium powder laid along the bottom of the tube is shaken away from
antinodes but left undisturbed at the nodes
You can investigate factors a ecting the resonant frequencies of a string:
fl fl fi ff fffl fi fi fi fi fl fi
A stationary wave is the superposition of two progressive waves with the same frequency
(wavelength), moving in opposite directions
- no energy is transmitted by a stationary wave
- You can demonstrate stationary waves by setting up a driving oscillator at one end of a
stretched string with the other end xed the wave generated by the oscillator is re ected back
and forth
- For most frequencies the resultant pattern is a jumble. However, if the oscillator happens to
produce an exact number of waves in the time it takes for a wave to get to the end and back
again, then the original and re ected waves reinforce each other.
- At these “resonant frequencies” you get a stationary wave where the pattern doesn’t move
Stationary waves in strings form oscillating loops separated by nodes:
Nodes are where the amplitude of the vibration is zero.
Antinodes are points of maximum amplitude .
An exact number of half wavelengths ts onto the string:
- First Harmonic: this stationary wave is vibrating at the lowest possible resonant frequency. It
has one loop with a node at each end.
- Second Harmonic: it is twice the frequency of the rst harmonic. There are two loops with a
node in the middle and one at each end
- Third Harmonic: is three times the frequency of the rst harmonic. 1 1/2 wavelengths t on the
string
Between two nodes every part of the wave is in phase, across a node the parts of the wave are
180 degree out of phase
You can demonstrate stationary waves with microwaves and sounds:
- microwaves re ected o a metal plate set up a stationary wave: microwave stationary wave
apparatus. You can nd the nodes and antinodes by moving the probe between the transmitter
and re ecting plate
- powder can show stationary waves In a tube of air: stationary sound waves are produced in the
glass tube. The lycopodium powder laid along the bottom of the tube is shaken away from
antinodes but left undisturbed at the nodes
You can investigate factors a ecting the resonant frequencies of a string:
fl fl fi ff fffl fi fi fi fi fl fi
