Question

1. how many nodes, not including the endpoints, are there in a standing wave that is two wavelengths long? three wavelengths long?

Explanation:

Step1: Recall the formula for the number of nodes in a standing wave

The formula for the number of nodes \(n\) (excluding endpoints) in a standing wave of length \(L = N\lambda\) (where \(N\) is the number of wavelengths) is \(n = N - 1\).

Step2: Calculate for \(N = 2\)

When \(N=2\), using the formula \(n = N - 1\), we substitute \(N = 2\) into the formula. So \(n=2 - 1\).
$$n = 1$$

Step3: Calculate for \(N = 3\)

When \(N = 3\), using the formula \(n=N - 1\), we substitute \(N = 3\) into the formula. So \(n=3 - 1\).
$$n = 2$$

Answer:

For a standing wave that is two wavelengths long, the number of nodes (not including endpoints) is \(1\). For a standing wave that is three wavelengths long, the number of nodes (not including endpoints) is \(2\).