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Thanks for the help.

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In summary, two sine waves with the same frequency and amplitude but different phase shifts can still produce a standing wave. The addition of the two waves results in a waveform that fits the standing wave equation, and the phase shift does not affect this.

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Thanks for the help.

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wt is the phase shift

see http://en.wikipedia.org/wiki/Phase_(waves [Broken])

see http://en.wikipedia.org/wiki/Phase_(waves [Broken])

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the addition is y= 2Acos(wt-phi/2)sin(kx+phi/2) where phi is the phase shift between 0 and 2pi. Does this still fit the standing wave equation y=(2Asin(kx))cos(wt) meaning its a standing wave or does the difference in phase shift mean they do not create a standing wave?

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sin(x) + sin(y) = 2·sin[(x+y)/2]·cos[(x-y)/2]

Bob S

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Your equations will be easier to read if you typeset them in LaTeX.

Yes, the equation you give is a standing wave. If you start with

[itex] \Psi(x,t) = A\cos(\omega \left[t-t_0\right]) \sin (k\left[x-x_0\right]) [/itex]

you can just define a new time coordinate and new space coordinate by

[itex] t' = t - t_0 [/itex]

[itex] x' = x - x_0 [/itex].

Then your original equation is just

[itex] \Psi(x',t') = A \cos(\omega t')\sin(k x')[/itex],

showing that the waveform is exactly the same as the standing wave you're used to.

A sine wave is a type of periodic function that describes a smooth and repetitive oscillation. In standing wave analysis, sine waves are used to represent the oscillating displacement of particles in a medium, such as a string or air column.

To create a standing wave, two or more sine waves with the same frequency and amplitude are added together. The resulting wave will have points of constructive and destructive interference, creating a stationary pattern.

The wavelength of a standing wave is equal to twice the length of the medium, divided by the number of nodes (points of zero displacement). The frequency of a standing wave is determined by the speed of the wave and the wavelength, and is inversely proportional to the wavelength.

The amplitude of a standing wave is determined by the amplitudes of the individual sine waves that are added together. The amplitude at each point of the standing wave is the sum of the amplitudes of the component waves at that point.

Standing waves have many practical applications, such as in musical instruments, where they produce distinct tones and harmonics. They are also used in medical imaging, such as ultrasound, and in telecommunications for signal transmission. Standing waves can also be found in natural phenomena, such as ocean waves and seismic waves.

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