Two sinusoidal waves combining in a medium are described by the equations
`y_1 = (3.0 cm) sin pi (x+ 0.60t)`
and `y_2 = (3.0 cm) sin pi (x-0.06 t)`
where, x is in centimetres and t is in seconds. Determine the maximum displacement of the medium at
(a)x=0.250 cm,
(b)x=0.500 cm and
(c) x=1.50 cm.
(d) Find the three smallest values of x corresponding to antinodes.

Answer

A, B, C, D

Explanation

`y=y_1 + y_2 = (6.0 cm) sin (pix) cos (0.6 pit)`
`:. A_x = 6.0 cm sin (pix)` …………(i)
In parts (a), (b) and (c) substitute the given
values of x and find the displacement
amplitude at these locations.
At antinodes
`A_x` = maximum = `+- 6.0 cm `
`:. pix = pi/2, (3pi)/2, (5pi)/2`
or `x= 0.5 cm, 1.5 cm, 2.5cm`.