KinexiaLEARN PHYSICS

Wave Period — Guitar String (Worked Example)

Easy
Problem

The low A string of a guitar vibrates at 110 Hz. What is the period of its vibration?

Given

  • f = 110 Hz

Find

The period T.

Principle

One period is the time for one complete vibration: T = 1/f.

Formula

Solution

  1. Write the formula: T=1/fT = 1/f

  2. Substitute: T=1/110T = 1/110

  3. Calculate: T=0.00909 s=9.09 msT = 0.00909\ \mathrm{s} = 9.09\ \mathrm{ms}

9.09 ms

Unit check

1 ÷ Hz = s — correct.

What this means physically

9.09 ms per swing — four times slower than the 440 Hz tuning fork, which is exactly why it sounds two octaves lower (each octave halves the frequency).

Common mistake

Mixing up period and frequency. If your 'period' comes out larger than 1 s for an audible sound, you computed f instead of T.