Question

For standing waves on a string, derive the relationship that correctly describes the locations of where the nodes will be.

Options:
a) Every odd multiple of λ/4
b) Every even multiple of λ/2
c) At λ intervals
d) At random positions

Answer 1

The nodes in standing waves on a string are located at every odd multiple of λ/4.

Step-by-step explanation:

In the case of standing waves on a string, the locations of the nodes can be derived using the relationship of every odd multiple of λ/4 (option a).

In a string with fixed ends, there must be a node at each end. The first mode (n = 1) has half a wavelength, so the distance between the nodes is equal to λ. As the mode number increases, the number of nodes and antinodes increases.

For example, for the second mode (n = 2), there will be two nodes and one antinode, resulting in a wavelength equal to twice the distance between the nodes.