A wave is decribed by the equation `y = (1.0mm) sin pi ((x)/(2.0cm) - (t)/(0.1s)). (a) Find the time period and the wavelength ? (b) Write the equation for the velocity of the particles. Find the speed of the particle at x = 1.0cm at time t = 0.01s, (c ) What are the speeds of the particles at x =3.0 cm 5.0 cm aned 7.0cm at t = 0.01 ? (d) What are the speeds of the particles at x = 1.0 cm at t= 0.011, 0.012, and 0.013s ?

Answer

A, B, C, D

Explanation

`Y = (1mm) sin pi[(x)/(2) cm -(t)/(0.01)sec]` (a) `T = 2xx0.01 = 0.2 sec = 20 ms`
`lambda= 2xx2= 4 cm`
(b) `upsilon = (dy)/(dt) = (d)/(dt) [sin2pi((x)/(4) -(t)/(0.02))]`
`=-cos 2pi {((x)/(4)) - ((t)/(0.02))} xx (1)/(0.02)`
`rArr v = -50 cos 2pi {((X)/(4)) - ((t)/(0.02))}`
at x = 1 and t = 0.01 sec,
`upsilon = -50 cos 2pi{(1)/(4) - (1)/(2)} = 0`
(c ) (i) at x = 3cm, t = 0.01 sec,
`u = - 50 cos 2pi{(3)/(4) - (1)/(2)} = 0`
(ii) `at x = 5cm, t = 0.01 sec,`
`upsilon = 0 (putting the values)`
at x = 7 cm, t =0.1 sec,
`upsilon = 0`
at x = 1cm, t = -0.011 sec,
`upsilon = 50 cos ((3pi)/(5)) = - 9.7 cm//sec`
(similarly the other two can be calculated).