What defines a harmonic wave?
A wave generated by a source that is undergoing simple harmonic motion
Source: http://hyperphysics.phy-astr.gsu.edu/hbase/waves/funhar.html
Harmonic Wave (Sinusodial Wave)
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Source: http://hyperphysics.phy-astr.gsu.edu/hbase/waves/funhar.html
Crest
Trough
Harmonic Wave (Sinusodial Wave)
Wavelength
Comment on the wavelengths of the plots.
Wavelength is decreasing from the red plot to the purple plot.
EquationTranverse displacement of the
element of the spring located at x: D(x) = A sin (kx) at t=0 Where A = amplitude k = wave number
Wave number k = 2π/λ-how often a waveform repeats itself (usually in rad/m)
Wave NumbersCompare the wave numbers (k) for the waveforms on the diagram.
A. k1 < k3 < k2
B. k3 < k2 < k1
C. k1 < k2 < k3
D. k2 < k1 < k3
1
2
3
Wave NumbersCompare the wave numbers (k) for the waveforms on the diagram.
A. k1 < k3 < k2
B. k3 < k2 < k1
C. k1 < k2 < k3
D. k2 < k1 < k3
1
2
3
Note: Wave number is defined by how often a waveform repeats
over a wavelength
TravelingHarmonic WavesHarmonic WavesEquation: Replace x
with x-vt for increasing x and x+vt for decreasing x
D(x,t)=A sin (k(x-vt)) orD(x,t) = A sin (k(x+vt))
v = wave speedt = arbitrary time
QuestionWhich of the following equations does NOT describe a traveling harmonic wave?
A. D (x,t) = A sin (x - 9t - 10)
B. D (x,t) = A cos (x^2 - 9t)
C. D (x,t) = A cos (x - 9t - 10)
D. D (x,t) = A sin (x + 9t)