HarmonicHarmonicWavesWavesWavesWaves

Physics 101Physics 101

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

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)

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)

not in the form x-vt or x+vt