In a standing wave, there are an integral number of nodes between any two nodes.
In a standing wave, nodes are the points of minimum or zero displacement from the mean position; moreover, amplitude is minimum or zero at the nodes.

Here is a diagram showing a node and an antinode in a stationary wave.

The mode of vibration is the various ways a string can vibrate if simply plucked without any boundary condition.

First mode of vibration:
- The first mode of vibration is the simplest normal mode, in which the string vibrates in a single loop. In other words, the waves consist of an antinode between two nodes.
- The wavelength of the first mode of vibration is λ = 2L, where L is the length of the wire/string.
- The frequency of the first mode of vibration, f = $\frac{\text{V}}{\text{2L}}$
- It is mostly known as the fundamental mode of vibration.
Second mode of vibration
- The second mode of vibration is the second harmonic, where the string vibrates in two loops. In other words, the wave consists of two antinodes and three nodes.
- The wavelength of the second mode of vibration is λ = L, where L is the length of the wire/string
- Frequency of the vibration, f = $\frac{\text{V}}{\text{L}}$

For those standing waves formed on strings that have nodes at both ends or antinodes at both ends:
- Frequency, f = n×f_o, where f_ois the frequency of the fundamental mode of vibration.
- Wavelength, λ = $\frac{\lambda_{0}}{n}$, where λ₀is the wavelength of the fundamental mode of vibration.
For those standing waves that have nodes at one end and antinodes at the other ends:
- Frequency, f = (2n-1) ×f_o, where f_ois the frequency of the fundamental mode of vibration.
- Wavelength, λ = $\frac{\lambda_{0}}{2n – 1}$, where λ₀is the wavelength of the fundamental mode of vibration.

Phase difference of stationary waves
- In a stationary wave, the phase difference between two successive nodes is 180^oor out of phase.
- In a stationary wave, the phase difference between two alternate nodes is 360^oor in phase.
- In a stationary wave, any adjacent points between the successive nodes are in-phase, whereas the points that are separated by a node have a phase difference of 180⁰.

The resonance can only occur when one object vibrates at the same natural frequency of a second object.
The velocity of sound can be found experimentally by applying resonance and the stationary wave.

The experimental setup to find the velocity of sound is shown here.

8.02 - Stationary Waves II

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