Standing Waves Formula Question

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SUMMARY

The discussion centers on identifying the term in the standing wave equation that represents the wave propagating to the left. The equation provided is Y(x,t) = Asin(2π(t/T - x/λ)) + Asin(2π(t/T + x/λ)). The term Asin(2π(t/T + x/λ) is confirmed to represent the leftward propagating wave, as the positive sign in the sine function indicates a shift to the left. Additionally, the relationship between the partial derivatives of the wave function is mentioned as a method to verify wave propagation direction.

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  • Understanding of wave mechanics and standing waves
  • Familiarity with trigonometric functions and their properties
  • Knowledge of calculus, specifically partial derivatives
  • Basic concepts of wave parameters such as amplitude, wavelength, and tension
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jessedevin
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Homework Statement


In the equation describing the superposition of the two waves to obtain a standing wave, which term represents the wave propagating to the left?


Homework Equations



Y(x,t) = Asin2\pi(t/T - x/\lambda) + Asin2\pi(t/T +x/\lambda)

The Attempt at a Solution


I think its Asin2\pi(t/T +x/\lambda) because I remember in math that the + in the sin wave will shift it towards the left, but I am not sure. FYI:
T= Tension
t= rime
A= amplitude
\lambda= wave length
x=distance
 
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jessedevin said:
I think its Asin2\pi(t/T +x/\lambda) because I remember in math that the + in the sin wave will shift it towards the left, ...
Sounds good to me. Do you know calculus? You can also check the sign of
<br /> v<br /> =<br /> \frac{\frac{\partial{Y}}{\partial{t}}}{\frac{\partial{Y}}{\partial{x}}}<br />
 

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