A wave on a string is described by y(x, t) = 12.9 sin(0.443x - 11.9f) where x an
ID: 1558794 • Letter: A
Question
A wave on a string is described by y(x, t) = 12.9 sin(0.443x - 11.9f) where x and y are in centimeters and t is in seconds. (a) What is the transverse speed for a point on the string at x = 5.81 cm when t = 0.229 s? (b) What is the maximum transverse speed of any point on the string? (c) What is the magnitude of the transverse acceleration for a point on the string at x = 5.81 cm when t = 0.229 s? (d) What is the magnitude of the maximum transverse acceleration for any point on the string? (a) Number Units (b) Number Units (c) Number Units (d) Number UnitsExplanation / Answer
y = 12.9 sin (0.443x – 11.9 t) --------------- (1)
speed of particle
v(y) = dy/dt differentiating (1) with respect to time (t)
v(y) = (-153.51) cos (0.443x – 11.9 t) (-11.9)
At x= 5.81 cm, t = 0.229 s
v(y) = (-153.51) [cos (0.443)(5.81) – 11.9 t) - (11.9) (0.229) ]
(a) v(y) = - 153.51 cm/s
For this speed to be maximum, cos (0.443x – 11.9 t) = +1 or -1.
Maximum v(y) = v(max) = 153.51 cm/s
(b) v(max) = 153.51 cm/s
Accelaration at a point
d2y/dt2 = (-153.51) [ -sin (0.443x – 11.9t) ] (-11.9) double differentiating (1) with respect to time.
At x= 5.81 cm, t = 0.229 s
d2y/dt2 = 1826.7 [ -sin (0.443x – 11.9t) ]
= 58.8 m/s2
(c) d2y/dt2 = 58.8 m/s2