A uniform stretched string of length L is fixed at both ends and transverse waves on it have speed v. Which expression gives the frequency fₙ of the nth harmonic?
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A uniform stretched string of length L is fixed at both ends and transverse waves on it have speed v. Which expression gives the frequency fₙ of the nth harmonic?

G1 Physics · Accepted Answer

For a string fixed at both ends, both ends are nodes. The nth harmonic contains n half-wavelengths: L = nλₙ/2. Therefore, λₙ = 2L/n. Hence, fₙ = v/λₙ = nv/(2L). Correct option: A.