Superposition and Standing Waves
The goal of Chapter 16 has been to use the idea of superposition to understand the phenomena
of interference and standing waves.
The displacement of a
medium when more than one
wave is present is the sum of
the displacements due to each
Two identicallravel ing waves
moving in opposite directions
create a smnding wave.
---Node spacing is
The boundary conditions deter-
mi ne which standing-wave fre-
quencies and wavelengths are
allowed. The allowed standing
waves are modes of the system.
of intensity) are produced when two
waves of slightly different frequencie.
Loud Soft Loud Soh Loud Soft Loud
In general, the superposition of two or more waves into a single wave is called interference.
Constructive interference occurs when
crests are aligned wilh crests and troughs wilh
troughs. We say the waves are in phase.
occurs when the path-length difference
a whole number of wavelengths.
Destructive interference occurs when crests
are aligned with troughs. We say the waves
are out of phase.
occurs when the path-
is a whole number of
wavelengths plus half a wavelength.
A standing wave on a string has a
node at each end. Possible modes:
A standing sound wave in a tube can have
different bOllndary oonditions: open-open,
closed-closed, or open-closed.
= 1,3, 5,.
Standing waves are multiples of a
fundamental frequency, the frequency
of lhe lowest mode. The higher modes
are the higher harmonics.
For sound, the fundamental frequency
determines the perceived pitch; the
hi gher harmonics determine the tone
_____ Fundamental frequency
Our vocal cords create a range of har-
monics. The mix of higher harmonics is
changed by our vocal tract to create dif-
ferenl vowel sounds.
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