FULL SCREEN PRINTER VERSION BACK NEXT Chapter 16, Problem 062 A sinusoidal trans

Question

FULL SCREEN PRINTER VERSION BACK NEXT Chapter 16, Problem 062 A sinusoidal transverse wave traveling in the positive direction of an x axis has an amplitude of 3.4 cm, a wavelength of 18 cm, and a frequency of 260 Hz. If the wave equation is of the form what are (a) ym (b) k, and (c) w, (d) the correct choice of sign in front of w? What are (e) the maximum speed of a point on the cord and (f) the speed of the wave? (a) Number (b) Number (c) Number Units Units Units (e) Number Units (f) Number Units

Explanation / Answer

y(x, t) = ym*sin (kx - wt)

Part A

ym = amplitude = 3.4 cm = 0.034 m

Part B

k = wave number

k = 2*pi/lambda

lambda = wavelength = 18 cm = 0.18 m

k = 2*pi/0.18 = 34.91 m^-1

Part C

w = 2*pi*f

w = 2*pi*260 = 1633.63 rad/sec

Part D

Since the wave is traveling in +ve x-axis, So there will be -ve sign before w

negative sign

Part E

y = 0.034*sin (34.91x - 1633.63t)

Now

Vmax = A*w

Vmax = 0.034*1633.63 = 55.54 m/sec

Part F

wave speed

v = lambda/T = w/k

v = 1633.63/34.91 = 46.79 m/sec

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