Question

If y(x, t) = (5.2 mm) sin(kx + (520 rad/s)t + ϕ) describes a wave traveling along a string, how much time does any given point on the string take to move between displacements y = -2.0 mm and y = +2.0 mm?

Can someone do this, and explain how? I have a quiz on this subject matter soon and I have absolutely no idea how to do this, and I have almost no understanding of what is going on in this problem. Thank you in advance for any help you provide!

Answer 1

when y=-2 mm

$-2=5.2Sin\left ( Kx+520t +\phi \right )$

$=>Kx+520t+\phi =Sin^{-1}\left ( \frac{-2}{5.2} \right )=-0.3948---1$

when y=2 mm

$2=5.2Sin\left ( Kx+520t +\phi \right )$

$=>Kx+520t+\phi =Sin^{-1}\left ( \frac{2}{5.2} \right )=0.3948---2$

2-1

$=>Kx+520t+\phi-Kx-520t-\phi =0.3948-(-0.3948)$

$1040t =0.7896$

t=7.592*10^-4 s (or) 0.7592 ms