A transverse wave on a string is described by the following wave function. y = 0

Question

A transverse wave on a string is described by the following wave function. y = 0.105 sin 9 x + 3t where x and y are in meters and t is in seconds.

A transverse wave on a string is described by the following wave function ys 0.105 sin ( x + 3,t where x and y are in meters and t is in seconds (a) Determine the transverse speed at t = 0.230 s for an element of the string located at x-1.30 m. m/s (b) Determine the transverse acceleration at t = 0.230 s for an element of the string located at = 1.30 m. m/s2 (c) What is the wavelength of this wave? (d) What is the period of this wave? (e) What is the speed of propagation of this wave? m/s Need Help?Watch I -15 points SerPSE9 16.P.019.soln. My Notes Ask Your Teacher 7.75 cm, 85.0 cm, f (a write the expression for y as a function of x and t in SI units for a sinusoidal wave traveling along a rope in the negative x direction with the following characteristics: A 4.00 Hz, and y(0, t) = 0 at t = 0, (Use the following as necessary: x and t.) (b) write the expression for y as a function of x and t for the wave in part (a) assuming y(x, 0) = 0 at the point x 22.5 cm. (Use the following as necessary: x and t.)

Explanation / Answer

a) v = dy/dt = 3 pi*0.105* sin (pi x /9 + 3 pi t )

at the given time and location v = 3 pi*0.105* cos (pi*1.3/9 + 3 pi*0.23 )

= 0.9896 cos 2.6214

= -0.8586 m/s

b] a = dv/dt = (3 pi)^2*0.105* sin (pi*1.3/9 + 3 pi*0.23 )

= 9.32677 sin 2.6214

= 4.6358 m/s^2

c] wavelength = 2pi/k = 2pi/[pi/9] = 18 m

d] period T= 2pi/w = 2pi/[3pi]

= 2/3 = 0.667 s

e] speed of wave = wavelength/T

= 18*3/2

= 27 m/s answer

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