∴ ℷ + ℷ/4 = 0.5 ⇒ ℷ = 0.4m
Also, the velocity of waves produced in the rod,
v = √Y/p = √2 x 1011/8 x 103 = 5000 m/s
Since, amplitude of antinodes = 2 x 10-6 m
∴ 2a = 2 x 10-6 m ⇒ a = 10-6 m
The equation of wave moving in the positive X – direction will be
y1 = a sin 2π/ℷ (vt – x)
⇒ y1 = 10-6 sin 2π/0.4 (5000t – x)
The equation of wave after reflection and moving in X – axis is
y2 = 10-6 sin[ 2π/0.4 (5000t + x]
The equation of the stationary wave is
y = 2a cos 2π/ℷ x sin 2π/ℷ vt
∴ y = 2 x 10-6 cos (2π/0.4 x) sin (2π/0.4 x 5000t)
Equation of wave at x = 2 cm
y = 2 x 10-6 cos (2π/0.4 x 0.02 ) sin (2π/0.4 x 5000t)
y = 2 x 10-6 cos (0.1 π) sin (25000 π t)