Sinusoidal Waves homework help

[PhysLiz]

Homework Statement

Two transverse sinusoidal waves combining in a medium are described by the wave functions
y1 = 5.00 sin π(x + 0.900t)
y2 = 5.00 sin π(x − 0.900t)
where x, y1, and y2 are in centimeters and t is in seconds. Determine the maximum transverse position of an element of the medium at the following positions.
(a) x = 0.210 cm
(b) x = 0.520 cm
(c) x = 1.30 cm

(d) Find the three smallest values of x corresponding to antinodes. (Enter your answers from smallest to largest.)

Homework Equations

Equation of a standing wave: y = 2Asin(kx)cos(wt)

The Attempt at a Solution

by my calculations,
y1+y2 = 10sin(pi*x)*cos(0.9*pi*t)

and from here I'm a bit confused. I tried deriving (y1+y2) with respect to time, and setting this equal to zero in order to find the corresponding x-values , but I just ended up with 0-values so either I did it incorrectly or that's not the right method. Thank you in advance for any assistance!

 

[fzero]

You can certainly maximize the function by using derivatives, but you'd have to show your work to let us see where you went wrong. It's probably very useful to sketch sin and cos by hand and recall what angles are extrema and which are zeros. You can go back and verify those using derivatives.

 

[PhysLiz]

it turned out to be much simpler than I thought. no derivatives involved - just assume the cosine component = 1 and then plug and chug to solve for 10sin(pi*x) values. but thank you!