Question

The equation of a simple harmonic progressive wave is given by y = 4 sin π ( $\frac{t}{0.02} - \frac{x}{75}$ ) cm. Find the displacement and velocity of the particle at a distance of 50 cm from the origin and at the instant 0.1 second (all quantities are in c.g.s. units) (Ans : Displacement = 3.464 cm, Velocity of the particle = 3.14 m/s)

Answer 1

Given :

y = 4 sin π( t / 0.02 – x/ 75)

x = 50 cm,

t = 0.1 second

y = A sin π (t/T  -x/ λ )

The given equation is, y = 4 sin π (t/  0.02 – x/ 75 )

y = 4 sin π( 0.1 /0.02 – 50/75)

= 4 sin π( 5 – 2/3)  

= 4 sin(  5 π – 2 π/3)

= 4 sin [4 π+[ π -2π/3)]

= 4 sin[ 4 π + π/3]

= = 4 sin 600  

∴ y = 4 × √3 /2 = 2 x√ 3 = 2 × 1.732  

∴ y = 3.464 cm

Velocity of particle v is given by  

v = dy dt  

= d /dt [x4sin π(t/ 0.02- x/ 75]

= 4 [ cos π[t/ 0.02-x/ 15)] π /0.02

 = 4[ cos π(5-2/3)( π/0.02)

=4[cos (5 π-2 π/3) π/0.02

=4[cos(4 π+ π-2 π/3)]( π/0.02)

=4[cos(4 π+ π/3)) π/0.02

=4cos[π/3)x π/0.02

=4x1x3.14/2x0.02

=314cm/s

V=3.14m/s

Answer 2

Explanation:

here is the answer for you dear!!!