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Chapter 16, Problem 053 A string oscillates according to the equation y= (0.425 cm) sin[(n/4.0 cm)x] cos[(47.5 n s1)t] What a

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Answer #1

compare the given equation with,

y = A*sin(k*x)*cos(w*t)

A = 0.425 cm
k = pi/4 rad/m
w = 47.5*pi rad/s

a) Amplitude = 0.425 cm (or) 0.0425 m <<<<<<<<--------------Answer

b) speed of the wave, v = w/k

= 47.5*pi/(pi/4)

= 190 cm/s (or) 1.90 m/s <<<<<<<<--------------Answer

c) wavelength, lamda = 2*pi/k

= 2*pi/(pi/4)

= 8 cm

distance between nodes = lamda/2

= 8/2

= 4.0 cm (or) 0.04 m <<<<<<<<--------------Answer

d) v = dy/dt

= 0.425*sin(pi*x/4)*(-sin(47.5*pi*t))*47.5*pi

= -0.425*47.5*pi*sin(pi*x/4)*sin(47.5*pi*t)

at x = 1.60 cm, t = 1.05 s

v = -0.425*47.5*pi*sin(pi*1.6/4)*sin(47.5*pi*1.05)

= 23.1 cm/s (or) 0.231 m/s <<<<<<<<--------------Answer

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