A string fixed at both ends has length 1 m and wave speed 168 m s⁻¹. It vibrates in harmonic n = 4. Determine the wavelength and frequency.

Question

Accepted Answer

0.5 m; 336 Hz Both fixed ends are displacement nodes, so harmonic n = 4 fits 4 half-wavelengths into the string: L = nλ/2. Rearranging and substituting gives λ = 2L/n = 2(1)/4 = 0.5 m. Wave speed, frequency and wavelength obey v = fλ, so f = v/λ = 168/0.5 = 336 Hz. The equivalent resonance relation fₙ = nv/(2L) produces the same frequency, checking that the stated harmonic has been counted correctly.

String resonance 6

A string fixed at both ends has length 1 m and wave speed 168 m s⁻¹. It vibrates in harmonic n = 4. Determine the wavelength and frequency.

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