Standing Waves Formula Question

[jessedevin]

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

 

[turin]

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
$$v = \frac{\frac{\partial{Y}}{\partial{t}}}{\frac{\partial{Y}}{\partial{x}}}$$

 

[thomate1]

Your understanding is correct. In this equation, the term Asin2\pi(t/T +x/\lambda) represents the wave propagating to the left. This is because the positive sign in front of the x term indicates that the wave is moving in the negative x direction. Similarly, the term Asin2\pi(t/T - x/\lambda) represents the wave propagating to the right, as the negative sign in front of the x term indicates movement in the positive x direction. This is a key feature of standing waves - the combination of two waves propagating in opposite directions creates a stationary pattern.