What are the three longest wavelengths for standing waves on a270-cm-long string that is fixed at both ends

The three longest wavelengths for the standing waves on a 270-cm long string that is fixed at both ends are:

1. 5.4 meters.

2. 2.7 meters.

3. 1.8 meters.

Given the following data:

To determine the three (3) longest wavelengths for these standing waves:

Mathematically, the wavelength for standing waves is given by the formula:

Where:

Note: n = 1, 2, and 3.

When n = 1:

When n = 2:

When n = 3:

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The answer is below

Explanation:

a) What are the three longest wavelengths for standing waves on a 270-cm-long string that is fixed at both ends? b. If the frequency of the second-largest wavelength is 50.0 Hz, what is the frequency of the third-longest wave length?

Solution:

a) The wavelengths (λ) for standing waves is given by the formula:

b) The frequency (f) and wavelength (λ) is given by:

fλ = constant

Hence: