standing waves (lo)

Standing WavesPhys 101 Learning Objects

Carly Chui

What is a standing wave?

special case of interference when 2 waves meeting are:

of the same amplitude

of the same frequency

traveling in opposite directions

To demonstrate how a standing wave is created, the following slides show a series of diagrams showing how it happens

by considering 2 transverse waves traveling in opposite directions along a stretched rope

red line = wave 1 moving to the right blue line = wave 2 moving to the left

green line = total

Here, the blue and red line are overlapped, so only the blue line can be seen

red line = wave 1 moving to the right blue line = wave 2 moving to the left

green line = total

Wave 1 moves to the right, while wave 2 moves to the left, while the maximum displacement of the wave is smaller than the previous as

the waves 1 and 2 are not overlapping

red line = wave 1 moving to the right blue line = wave 2 moving to the left

green line = total

As wave 1 and 2 are exactly opposite each other, the total wave is flat (on the x-axis)

red line = wave 1 moving to the right blue line = wave 2 moving to the left

green line = total

Wave 1 and 2 each move to the right and to the left, while the total wave is at its maximum or minimum when waves 1 and 2

intersect.

red line = wave 1 moving to the right blue line = wave 2 moving to the left

green line = total

The waves are overlapped again, giving double the amplitude for the total wave compared to the wave 1 and wave 2.

As a result of the above diagrams, the plot of the total wave (total displacement vs. distance) will be:

nodes = point on the rope that are always at rest

nodes

anti-nodes

antinodes = points where the maximum movements take place

* The three colours (green, red, blue) now correspond to different times. The string oscillates up and down

the resulting standing wave has its name:

its wave pattern remains fixed in space

only the displacement that changes over time

To enhance the understanding towards standing waves, the following compares

it with a normal travelling wave:

all points on the wave have different amplitudes

maximum amplitude at the antinodes, 0 at the nodes

Amplitude

Standing wave: Normal traveling wave

all points on the wave have the same amplitude

Frequency

Standing wave: Normal traveling wave

all points oscillate with the same frequency

all points oscillate with the same frequency

Wavelength

Standing wave: Normal traveling wave

twice the distance from one node/ antinode to the next node/antinode)

shortest distance (m) along the wave between 2 points that are in phase with one another

Phase

Standing wave: Normal traveling wave

all points between one node and the next node are moving in phase

all points along a wavelength have different phases

Energy

Standing wave: Normal traveling wave

energy is not transmitted through wave

BUT - has energy associated with it

energy is transmitted by the wave