Question

Two sinusoidal waves combining in a medium are described by the following wave functions, where x is in centimeters and t is in seconds.

y₁ = (1.0 cm) sin π(x + 0.40t)
y₂ = (1.0 cm) sin π(x - 0.40t)

Determine the maximum transverse position of an element of the medium at the following positions.

(a) x = 0.270 cm
cm
(b) x = 0.660 cm
cm
(c) x = 1.50 cm
cm
(d) Find the three smallest values of x corresponding to antinodes.
cm (smallest)
cm (second smallest)
cm (third smallest)

Answer 1

Page Sol y = yıt ya y = 1 sina (n + 0.4+) + sina (n + 0.4+) After Solving ing nomertory Identity: 2 (sinan) x cos (0,4 kt) (for the maximum value; cos o 4t - 1 2 sinan (a.) At n = 0.27 enn A (n=0.27) = 2 sin (A x 0.27) - 1.50 am :. A max (M= 0.27) = 1.50 am At n = 0.66 cun; A (n20.66) = 2 sin (AXO,75) - 1.44 1 Amax (n = 0.66) = 1.414 am

c. Antinodes occur , when; Isin tal = An A, B1, SA , etc lie. In=o.sum, 1.5cm, 2, sun