Deck 2: Stationary Waves & Harmonics in tab-delimited format

What is a stationary wave?

A wave formed by the superposition of two progressive waves of the same frequency and amplitude travelling in opposite directions.

What is a node?

A point on a stationary wave where the displacement is always zero.

What is an antinode?

A point on a stationary wave where the displacement reaches a maximum.

How are stationary waves formed on a string?

By interference between two waves of the same frequency and amplitude moving in opposite directions.

What causes nodes and antinodes in a stationary wave?

Constructive and destructive interference at fixed points.

What is the fundamental frequency on a stretched string?

The lowest possible frequency at which a stationary wave can form, with one antinode and two nodes.

How many loops does the 2nd harmonic have on a string?

2 loops (or 2 antinodes and 3 nodes).

What is the wavelength of the 1st harmonic on a string of length L?

λ = 2L

What is the wavelength of the 2nd harmonic on a string of length L?

λ = L

What is the wavelength of the 3rd harmonic on a string of length L?

λ = 2L/3

What is the general formula for the wavelength of the nth harmonic?

λ = 2L / n

What is the general formula for the frequency of the nth harmonic on a string?

f = n(v / 2L)

What is required at both ends of a vibrating string?

Nodes, because the ends are fixed.

What is the fundamental frequency in a closed pipe?

The stationary wave has a node at the closed end and an antinode at the open end.

What is the wavelength of the fundamental frequency in a closed pipe of length L?

λ = 4L

What harmonics are present in a closed pipe?

Only odd harmonics: 1st, 3rd, 5th…

What is the wavelength of the 3rd harmonic in a closed pipe?

λ = 4L / 3

What harmonics are present in an open pipe?

All harmonics (1st, 2nd, 3rd, …) are present.

What boundary condition exists at an open end of a pipe?

An antinode forms at an open end.

How many wavelengths are shown in a stationary wave with 3 loops?

1.5 wavelengths.

If a stationary wave has 3 antinodes, which harmonic is it?

3rd harmonic.

If a string is vibrating in its 4th harmonic, how many nodes are present?

5 nodes.

Equation linking wave speed, frequency, and wavelength?

v = fλ

What affects the speed of a wave on a string?

The tension and mass per unit length of the string.

What type of wave is sound in air?

A longitudinal wave that can form stationary waves in pipes.

Why do only certain frequencies form standing waves?

Because only specific frequencies satisfy the boundary conditions (resonance).