A sinusoidal transverse wave is traveling along a string toward decreasing x. Th

Question

A sinusoidal transverse wave is traveling along a string toward decreasing x. The figure below shows a plot of the vertical (y) displacement of the string as a function of position along the string (x) at time t = 0. The string tension is 4.8 N, and its linear density is 18 g/m.

http://www.webassign.net/userimages/p270%20hw3%20prob%204%20new%20graph.jpg?db=v4net&id=209469

(a) According to the graph, what is the amplitude of the wave?
=5cm
(b) According to the graph, what is the wavelength of the wave?
=.4m
(c) Find the wave speed.
=16.32 m/s
(d) Find the period of the wave.
=???
(e) Find the maximum transverse speed of a point on the string, and indicate when it occurs:
=???
(f) Find the maximum size of the transverse acceleration of a particle on the string, and indicate when it
=???
(g) Fill in the equations below, describing the transverse displacement, velocity and acceleration of the string.
(Note: Please use positive phase angles.)

y(x,t)=(___m)sin(___m^-1 x(+/-)___s^-1 t+___rad)

vy(x,t)=(___m/s)cos(___m^-1 x(+/-)___s^-1 t+___rad)

ay(x,t)=(___m/s^2)sin(___m^-1 x(+/-)___s^-1 t+___rad)

Explanation / Answer

(a) 5 cm (b) 40 cm = 0.4 m (c) 16.3299 m/s (d) 24.4949 ms (e) 12.825498 m/s (f) 3289.868 (m/s^2) (g) (k = rac{2pi}{40} cm^{-1} ) (omega = rac{2pi}{24.4949} rad/ms = 256.509966 rad/s ) (delta = 53^o = 0.9250 rad) (y(x,t)=A sin(kx pm omega t + delta) ) (A = 0.05m) (v = dot{y}(x,t) = pm A omega cos(kx pm omega t + delta) ) (A omega = 12.825498 m/s ) (a = ddot{y}(x,t) = - A omega^2 sin(kx pm omega t + delta) ) (A omega^2 = 3289.868 m/s^2)

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