What are the key components of sinusoidal wave equations?

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The discussion focuses on understanding sinusoidal wave equations, specifically the equation y(x,t)=(5.5 mm)sin(12.0x -2.0 s-1 * t+0.390 rad). The wavelength (λ) is determined to be 0.524 m, calculated using the formula (2π)/k, where k is the wave number (12 in this case). The phase difference between the two waves is indicated by the additional phase term of 0.390 rad. Participants express confusion about the equation's structure and seek clarification on the significance of its components. Understanding the general form of traveling waves and the trigonometric identities for combining sine functions is also emphasized.
Mr Krabs
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Member advised to use the homework template for posts in the homework sections of PF.
Two sinusoidal waves, identical except for phase, travel in the same direction along a string, producing the net wave

y(x,t)=(5.5 mm)sin(12.0x -2.0 s-1 * t+0.390 rad),


A. with x in meters and t in seconds. What is the wavelength λ of the two waves?
B. What is the phase difference between them?
C. What is their amplitude ym?


I know A is .524 m but I am not too sure why. Other than that, I don't really know what I am doing. My general issue here is that I do not fully understand the form of the equation. Any information on what the different terms in the equation do would be helpful.

I got the answer for A from (2pi)/12 btw. The 12 was the coefficient of the first term, but again I don't really understand what is happening here.
 
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Mr Krabs said:
I know A is .524 m but I am not too sure why.
The wavelength is the smallest nonzero change in x which completes a cycle, i.e. changes the argument to the sine function by 2π.
Mr Krabs said:
I do not fully understand the form of the equation.
Write a general equation for a traveling wave. Write a second one which only differs in phase. Write the sum of the two.
What trig formulae do you know that can put the sum of two sine functions in a different form? (These should be listed in the Relevant Equations section of the template. Oh, you didn't keep the template. Tut tut.)
 
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