Physics Notes – Standing Waves

A standing wave is a pattern of interference that occurs when identical waves travel in opposite directions through the same medium. (This is most often a result of waves approaching a boundary and at the same time reflecting off of that boundary in the opposite direction.)

In any standing wave there will be nodes and antinodes:

A node is a point in the medium at which there is zero disturbance. A node is a site of continuous and total destructive interference and the medium does not oscillate at that point.

An antinode is a point in the medium at which the amount of disturbance is maximized. An antinode is a site where constructive interference occurs and the oscillations of the medium are greatest.

The wavelength of any standing wave is equal to twice the distance between successive nodes or twice the distance between successive antinodes.

The speed of a standing wave is the speed at which that particular type of wave travels through the medium. (Even though the standing wave pattern is stationary it is being produced by waves that are traveling with a particular speed through the medium.)

Any standing wave system (such as a string or column of air) can only sustain standing waves at particular frequencies. These patterns of vibration that are unique to the system are called its harmonics (also sometimes called overtones). The harmonic with the lowest frequency is called the fundamental. It is a property of standing waves that any harmonic frequency is an integer multiple of the fundamental frequency.

String or cable fixed rigidly at both ends:

Examples: guitar string, suspension cable, electrical cable between poles, etc.

Each end is a node.

Number of antinodes = n

Number of nodes = n + 1

n = 1, 2, 3, 4 . . .

Pipe open at both ends (column of air):

Examples: flute and many wind instruments, culvert, etc.

Each end is an antinode.

Number of nodes = n

Number of antinodes = n + 1

n = 1, 2, 3, 4 . . .

Pipe open at one end, closed at other end:

Examples: reed instrument, certain organ pipes, straw in a drink, etc.

Open end is an antinode.

Closed end is a node.

Number of antinodes =

Number of nodes =

n = 1, 3, 5, 7 . . .
(only odd harmonics occur!)