A guitar string of length 0.68 m is fixed at both ends and carries transverse waves at 340 m/s. Calculate the frequency of its fundamental (lowest) mode.

Vibrations & Waves Challenge #3 — Standing Waves

A standing wave
on a guitar string.

Vibrations & Waves Medium

Problem

A guitar string of length 0.68 m is fixed at both ends. Transverse waves travel along it at 340 m/s. Calculate the frequency of its fundamental (lowest) mode of vibration.

String length\( L = 0.68\ \mathrm{m} \)
Wave speed\( v = 340\ \mathrm{m/s} \)
Fundamentalhalf a wavelength fits on L
Answer inhertz

Both ends are nodes — that fixes the wavelength before anything else.

Hint: in the fundamental, the string holds exactly half a wavelength between its fixed ends, so \( \lambda = 2L \). Then the wave equation \( f = \tfrac{v}{\lambda} \) finishes the job.

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A standing waveon a guitar string.

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A standing wave
on a guitar string.