Question

NOTES ASK YOUR TEACHER PRACTIC The wae functie for a standing wave on a string is described by (x, t) - 0.017 sid(4x) cos(52nt). where andre in meters and t is in seconds. Determine the maximum displacement and maximum speed of a point on the string at the following positions. (a) x 0.10 m Yma m/s m x = 0.25 m x = m m/s (C) x 0.30 m Ymax m m/s (d) x 0.50 m max max m m/s

Answer 1

Differentiate the wave function to find the value of the speed and use that to find the required maximum displacement and maximum speed as shown below

- at a) y (xt) y (35t) = 0.017 sin (4 1xc) cos(s2t) v (art) = dy 0.017 sin (sin41x) (-sin(522t)) (525) V = -2.78 singh x) sin szat) So, at ac, Imax 0.017 sin(473) {when cos(szat) = 1 [2.78) sin 4730) { When sin(szłt)=1 = and Umas = at x=0.1, Ymasc 0.017sinkt 1 (0-1)) was speed, Umar ( 2.78) sin(4R0.2)) = = 10.0162 m こ = 2.64 m/s at x = 0.25 Ymase = = o m 0.017sink 76.25)) (278) sin(4x(-25)) こ masc. speed Vinanc = با ما | 0 c ) at x=0.3 / = 0.00 999 m Ymase mas speed, Umar 0.017sink416o-3)) (2.78) sin(4x(0,3)) 2 = 1.63 m/s at x = 0.5, Ymase 0.017sinkł(o.5)) mas speed, ( 2.78) sin(4x(0.5)) - = 0 Viman こ olmis