FE Physics
Formulas & Explanation

Dutch version

Standing waves

Cause : resonance.

Standing transverse waves

Form: sine .

Occurs in stringed instruments

Amplitude varies along the string. They all the vibrate with the same frequency.

Nodes  (no vibrations)  and  Antinodes (amplitude maximal value)

Nodes at the fixed ends and between the antinodes.

Between two nodes vibrate the points with equal phase

Δφ = 0 ( points between two nodes) or 0.5 (points on either side of a node)

There is also:

v = f λ      ( v speed of the travelling wave in the string)

λ length of one sine

Standing waves in a string fixed at two ends

Example 1

A string with length of 60 cm is fixed at both sides

The fundamental has a frequency of  400 Hz.

Calculate the speed of the wave in the string.

The distance  from node to node  N-N  = ½ λ     So  0.5 λ1= 0.60 m         λ1 = 1.20 m

λf is the wavelength of the fundamental  mode

v = f1  λ1  = (400)( 1.20) = 480 m/s

Example  2

Find now the frequency of the second harmonic

v  = f2 λ2

λ2 = 0.60 m

480 = f2 0.60         f2= 800 Hz

The  frequency of the third harmonic   is 1200 Hz       ( 1.5 λ3 = 0.60 m

λ3=  0.40 m)