A wave is described by the equation Y = (1.0 mm) sin p (x/(2.0 cm)-t/(

QUESTION

A wave is described by the equation
Y = (1.0 mm) sin p (x/(2.0 cm)-t/(0.01 s)).
(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 = 1.0 cm at time t = 001 s. (c) What are the speeds of the particles at x = 3.0 cm, 5.0 cm and 7.0 cm at t = 0.01 s?
(d) What are the speeds of the particles at x = 1.0 cm at t = 0.011, 0.012, and 0.013 s?
Sol. . Y = (1 mm) sin p [x/2cm t/0.01 sec] a) T = 2 ? 0.01 = 0.02 sec = 20 ms ? = 2 * 2 = 4 cm b) v = dy/dt = d/dt [sin 2p (x/4 t/0.02)] = cos2p x/4) (t/0.02) * 1/(0.02) ? v = 50 cos 2p (x/4) (t/0.02) at x = 1 and t = 0.01 sec, v = 50 cos 2* [(1/4) (1/2)] = 0 c) i) at x = 3 cm, t = 0.01 sec v = 50 cos 2p (3/4 ) = 0 ii) at x = 5¦

cm, t = 0.01 sec, v = 0 (putting the values) iii) at x = 7 cm, t = 0.01 sec, v = 0 at x = 1 cm and t = 0.011 sec v = 50 cos 2p (1/4) (0.011/0.02) = 50 cos (3?/5) = 9.7 cm/sec (similarly the other two can be calculated)

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