(a) Find the amplitude. m (b) Find the wavelength. m (c) Find the wave speed. m/

Question

(a) Find the amplitude.
m

(b) Find the wavelength.
m

(c) Find the wave speed.
m/s

(d) Find the period of the wave.
s

(e) Find the maximum speed of a particle in the string.
m/s

(f) Complete the equation describing the traveling wave, inwhich x and y are in metersand t is in seconds.
y(x, t) = sin( x + t + )
A sinusoidal transverse wave is traveling along a string in thenegative direction of an x axis. The figurebelow shows a plot of the displacement as a function of position attime t = 0. The x axis ismarked in increments of 5 cm andthe y axis is marked in incrementsof 5 cm. The string tensionis 3.1 N, and its linear densityis 31 g/m. (a) Find the amplitude. m (b) Find the wavelength. m (c) Find the wave speed. m/s (d) Find the period of the wave. s (e) Find the maximum speed of a particle in the string. m/s (f) Complete the equation describing the traveling wave, inwhich x and y are in metersand t is in seconds. y(x, t) = sin( x + t + )

Explanation / Answer

a) A = 5 * .05 =.25 m b) = 4 * .05 = .20 m c) v = (F / (m / L)) = (3.1 / .031) = 10 m /s d) f = v /     T = 1 / f = / v =.2 / 10 =.02 sec e) y = A sin t   variation of amplitude with time      (dy / dt)max = A =2 f A = 2 * 50 * .25 = 78.5 m/s f) y = A sin (k x + v t)      + signfor wave moving in negative direction (k = 2 /)    y = A sin (2 x / + v t + )to include the phase At t = 0   .8 = sin     sincethe amplitude is 80% of its maximum = 127 deg = 2.22rad     Since the wave is traveling to the left, at t = 0 it haspassed its maximum amplitude and has dropped to .8 * A

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