Standing and Stationary Waves on a String - A Level Physics

Unlike progressive waves that transfer energy, standing or stationary waves store energy and do not appear to move. They are formed by the interaction (superposition) of a progressive wave and its reflection off a boundary, producing a resultant wave.

When a string has fixed ends, movement at these points is constrained. These fixed points are called 'nodes,' where there is no displacement. Points of maximum displacement are called 'antinodes.' The video illustrates the first standing wave pattern, showcasing nodes at the ends and an antinode in the middle.

The video demonstrates how different standing wave patterns can be formed on a string of the same length. The second standing wave shown has nodes at both ends and in the middle, along with two antinodes. It explains that the distance from a node to an antinode is equal to half the wavelength (λ/2).

For a string of length 'L', the first standing wave is called the 'fundamental' or the first harmonic. Here, L = λ/2, so the wavelength is 2L. This corresponds to the fundamental frequency (F0). The second harmonic occurs when L = λ, meaning the frequency is twice the fundamental frequency. Subsequent harmonics (third, fourth, etc.) are multiples of the fundamental frequency, leading to various modes of vibration observed in musical instruments.

Standing waves exhibit multiple modes of vibration, known as harmonics, each characterized by specific nodes and antinodes. As the frequency increases, the wavelength decreases, resulting in more nodes and antinodes along the string.