Question

A sinusoidal wave in a string is described by the wave function

y = 0.155 sin (0.525x - 46.5t)

where x and y are in meters and t is in seconds. The mass per length of the string is 13.2 g/m.

(a) Find the maximum transverse acceleration of an element of this string.

(b) Determine the maximum transverse force on a 1.00-cm segment of the string.

(c) State how the force found in part (b) compares with the tension in the string.

PLEASE SHOW WORK TO ALL PARTS! Thanks!

Answer 1

given equation
y = 0.155 sin (0.525x - 46.5t)
compare with wave equation
y =A sin(kx-wt)
Amplitude A =0.155 m
wave number K = 0.525 m
ang velocity w = 46.5 rad/s
mass per unit lenght mu = 13.2 g/m =0.0132 kg/m
A)
maximum transverse acceleration a =-W^2*A

                                   = - 46.5^2*0.155 = - 335.148 m/s^2

------------------------------------------------------------------------------------
B)
the maximum transverse force on a 1.00-cm segment of the string
Fmax= mass *acceleration = lenght *mu *a

                                           = 0.01*0.0132*(-335.148) = - 0.044239 N = -44.2x10^-3 N

----------------------------------------------------------------------------------------------------
C)
wavespeed v = w/k = sqrt(T/mu)
46.5/0.525 = sqrt(T/0.0132)
Tension T = 103.55 N
Tension/Fmax = 103.55/0.044239 = 2340.75

------------------------------------------------------------------------------------------------------------