# Nodes and Antinodes for standing wave

In the arrangement shown in the figure below, an object of mass m can be hung from a string (linear mass density $\mu$ = 2.00 g/m) that passes over a light (massless) pulley. The string is connected to a vibrator with constant frequency $f$, and the length of the string between point P and the pulley is $L = 2.00 m$. When the mass m of the object is either 16.0 kg or 25.0 kg, standing waves are observed in the string.

No standing waves are observed for any other mass between these values.

$n$ = number of nodes from 25kg

$n + 1$ = number of nodes from 16kg

I do not understand why they have only integer 1 difference between the numbers of nodes of 25 and 16kg...

Anybody know why they put n + 1 for 16kg? If we do that, the problems becomes easy to solve.

Thanks,

## 1 Answer

The question says:

No standing waves are observed for any other mass between these values

So if you increase the mass smoothly from 16 to 25kg no standing waves are seen. If there was more than two nodes difference between 16 and 25kg you would have seen one or more standing waves as the mass was increased.