The nth harmonic of standing waves in a string of length L has a wavelength of 0.4889 m, while the (n − 1)th harmonic has a wavelength of 0.5500 m. Find L, the length of the string.

Answer 1

I will assume that the string is fixed at both ends.

In that case, the formula for the wavelength of the nth harmonic is λ_n = 2 L/n .

Two equations can be set up

.4889 = 2 L / n and

.550 = 2 L /( n -1)

or .4889 n = 2 L and

.550 (n-1) = 2 L

This is a set of two equations and two unknowns. Since the two right hand sides are the same ,

we have .4889 n = .550 ( n-1) . This is easy to solve giving n = 9 .

Substituting this value of n into the first equation gives L = 2.2