112. Calc A transverse wave propagates according to The following (SI units): y
ID: 1292874 • Letter: 1
Question
112. Calc A transverse wave propagates according to The following (SI units): y (x,t) = 0.1 sin(1.25x - 3.5t) (a) Calculate the value of y when x = 1 m and t 2 s. (b) If x = 3 m, at what time(s) does y = 0.08 m? (c) What is the maximum value of the transverse velocity of a point on the wave? (d) What is the maximum value of the transverse acceleration of a point on the wave? (e) What s the value of the transverse velocity when x = 2 rn and t = 4 s? (f) What is the value of the transverse acceleration when x = 2 m and t = 4 s?Explanation / Answer
a) y = 0.1*sin(1.25*1 - 3.5*2)= 0.0508 m
b)
0.08 = 0.1*sin(1.25*3 - 3.5*t)
1.25*3 - 3.5*t = arcsin(0.08/0.1)
t = (1.25*3 - arcsin(0.08/0.1))/3.5 = 0.806 s
c)
dy/dt = 0.1*-3.5*cos(1.25*x - 3.5*t)
dy/dt = -0.35*cos(1.25*x - 3.5*t)
max speed = 0.35 m/s
d)
dv/dt = 0.1*3.5^2*-sin(1.25*x - 3.5*t)
max a = 1.225 m/s^2
e)
v = -0.35*cos(1.25*2 - 3.5*4)=-0.169
f)
a = 0.1*3.5^2*-sin(1.25*2 - 3.5*4)= -1.07
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