Answer to Question #89777 in Physics for Shivam Nishad

Question

Stationary waves are produced in a medium
by the superposition of two waves
y1 = 0.05 sin (3π t - 2 x)
and y2 = 0.05 sin (3π t + 2 x)
where x and y are in metre and t in second.
Calculate the amplitude of the particle at
x= 0.5 m. Given cos (57.3°) = 0.54

Answer 1

$$y=y_1+y_2=0.05( \sin{ (3π t - 2 x)}+ \sin{ (3π t+2 x)})$$

$$y=0.05( 2\sin{ (3πt) \cos{2x}})$$

$$A(0.5)=0.1 \cos{2(0.5)}=0.054\ m$$