In a standing wave on a string, the distance between two adjacent nodes is equal to half the wavelength (λ/2) of the wave. Nodes are the points on a standing wave where the amplitude is always zero, meaning the string does not oscillate at those points.
To understand this relationship, we can consider the fundamental mode, also known as the first harmonic, of a standing wave on a string. In the fundamental mode, the string has the simplest pattern with a single antinode (the point of maximum displacement) in the middle and a node at each end.
In this mode, the length of the string (L) is equal to half the wavelength (λ/2). Mathematically, we can express this relationship as:
L = λ/2
By rearranging the equation, we can solve for the distance between adjacent nodes:
λ = 2L
Therefore, the distance between two adjacent nodes in terms of the wavelength is equal to twice the length of the string.
It's important to note that this relationship holds for the fundamental mode (first harmonic) of a standing wave on a string. For higher harmonics or modes, the pattern of nodes and antinodes becomes more complex, but the distance between adjacent nodes will still be related to the wavelength according to the same principle.