Standing Waves

Reflection of a Wave - A standing Wave

A wave enters from the left (a) and is reflected (dashed) from the termination point on the right (d). Now there are two overlapping waves that combine to form a standing wave (red), oscillating (g through k) in place.

• in-phase
• standing wave

This occurs when wave makes one complete trip along the length of the string
(distance = 2 L)in the same time as one period of oscillation.

Standing Wave on a String

(a) A standing wave on a string that has both ends fixed. (b) represents a composite of all the configurations demonstrated in (a).

Wavelength:

n = 1,2, 3, . . .

All harmonics are produced

Wave velocity:

Frequency:

f _n = n f ₁ : n = 1, 2, 3, . . .

Period of vibration:

Standing Waves in 2D (drum)

f ₁ : fundamental frequency depends

• on radius R of drum
• tension of membrane T
• material of membrane d

Overtones :

f ₂ = 1.59 f ₁ f ₃ = 2.13 f ₁