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Exercise:
A harmonic wave is described by the following function: yx t AOtimessinomOtimes t+kOtimes x+phO. abcliste abc What are the amplitude the frequency the wavelength and the propagation speed of the wave? abc At what time does the po at x  xrefO cross the equilibrium position for the first time? abcliste

Solution:
abcliste abc The amplitude is given by the factor in front of the sine function: A resultAO The angular frequency is the factor next to the time t: omega omO It follows for the frequency f fF fracompi resultfP The wave number is the factor next to the position x: k kO It follows for the wavelength: lambda laF fracpik resultlaP The propagation speed is v vF latimesf resultvP abc At the equlibrium position the argument of the wave function is an eger multiple of pi: omega t+k x+phi_ npi quad nin N Solving for the time leads to t tF quad nin N Since k x+phi_ ktimesxref+ph valP valpiPtimespi the lowest positive time t is found for nnminS: ssctmin fracnmimespi-ktimesxref-phomresulttP abcliste
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Exercise:
A harmonic wave is described by the following function: yx t AOtimessinomOtimes t+kOtimes x+phO. abcliste abc What are the amplitude the frequency the wavelength and the propagation speed of the wave? abc At what time does the po at x  xrefO cross the equilibrium position for the first time? abcliste

Solution:
abcliste abc The amplitude is given by the factor in front of the sine function: A resultAO The angular frequency is the factor next to the time t: omega omO It follows for the frequency f fF fracompi resultfP The wave number is the factor next to the position x: k kO It follows for the wavelength: lambda laF fracpik resultlaP The propagation speed is v vF latimesf resultvP abc At the equlibrium position the argument of the wave function is an eger multiple of pi: omega t+k x+phi_ npi quad nin N Solving for the time leads to t tF quad nin N Since k x+phi_ ktimesxref+ph valP valpiPtimespi the lowest positive time t is found for nnminS: ssctmin fracnmimespi-ktimesxref-phomresulttP abcliste
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Branches
Mechanical Waves
Tags
phase, propagation, wave, wave number, wavelength
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(2, default)
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0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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