Question

A 2 cm string that is fastened at both sides is plucked. what is the wavelength of the n = 3 standing wave?

Answer 1

The wavelength of the n = 3 standing wave on a string that is 0.02 m long with both ends fixed is 0.0133 m or 1.33 cm.

Step-by-step explanation:

The question pertains to the wavelength of the n = 3 standing wave on a string that is 2 cm or 0.02 m long when plucked, with both ends fixed. For standing waves on a string fixed at both ends, the wavelength (λ) for a given mode number (n) is given by the equation λ = 2L / n, where L is the length of the string. In the case of the third harmonic (n = 3), the wavelength is therefore calculated as λ = 2 × 0.02 m / 3 = 0.0133 m or 1.33 cm.

Answer 2

To determined the value of wavelength of the standing wave, we use the formula

`\lambda =(2L)/(n).`

Here,
`\lambda` is the wavelength, L is the string length and n is integer.

Given, n = 3 and L = 2 cm.

Substituting these values in above formula, we get

`\lambda = 2 * (2)/(3) = 1.33 \ cm`

Thus, the wavelength of the standing wave is 1.33 cm.