Sect. 11-11: Wave Reflection & Transmission
• Waves can be reflected from objects.
• Two waves can interfere with each other.

• 2d & 3d waves have wave
“fronts”:

Law of Reflection (Plane Waves)

Sect. 11-12: Interference (Superposition)
• 2 waves , similar wavelengths
• Spatial variation at different times.
•
Constructive:
“In Phase”
• Destructive: “Out of Phase”

• Principle of superposition: In a spatial region where 2 waves overlap, the resultant wave displacement
 algebraic sum of the amplitudes

Interference (Superposition)

Sect. 11-13: Standing Waves
•
Standing waves: When incoming & reflected waves interfere, standing waves can be set up.
–
Antinodes : Positions of maximum amplitude (constructive interference).
–
Nodes : Positions of minimum amplitude
(destructive interference).
– Only certain frequencies (or wavelengths) are allowed for standing waves!

Standing Waves

•
Fundamental or Natural or Resonant
Frequencies

Frequencies at which
(large amplitude) standing waves are produced.
• String: Has many resonant frequencies.
– Unlike spring-mass system, which has only one!

•
Standing waves on a string of length L .
• Still have: v = λf
• Recall, v is fixed by properties of the string.
v = [F
T
/(m/L)]
½
• The standing wave frequency f = (v/λ) or, alternatively, the wavelength
λ = (v/f) is fixed by the string length L!
– We need to fit the wavelength λ into the length L.
• We’ll focus on λ for standing waves
.

Standing Waves on a String

• General : String, length L , with both ends fixed, for standing waves we must have an integer multiple n of
(½)λ fit into length L:

L = (½)nλ n
, n = 1, 2, 3, 4, …

The only allowed wavelengths are:
λ n
= (2L)/n , n = 1, 2, 3, 4, …
• Still have: v =
λf with v fixed by the string properties v = [F
T
/(m/L)]
½

The only allowed frequencies (
 harmonic frequencies ) are: f n
= (v/λ n
) = (½)n(v/L) f
1
=
(½)
(v/L)
 fundamental frequency
 f n
= nf
1
, n = 1, 2, 3, 4, … ( Example 11-14)

Wave Refraction

Wave Diffraction