Chapter 16, Problem 022 A sinusoidal wave is traveling on a string with speed 55

Question

Chapter 16, Problem 022 A sinusoidal wave is traveling on a string with speed 55.6 cm/s. The displacement of the particles of the string at x = 22 cm is found to vary with time according to the equation y = (6 cm) sin[1.7 - (4.3 s-1)E]. The linear density of the string is 4.3 g/cm. What are (a) the frequency and (b) the wavelength of the wave? If the wave equation is of the form y(x,t) = ym sin(kx - wt), what are (c) Ym (d) k, and (e) w, and (f) the correct choice of sign in front of w? (9) What is the tension in the string? Units Units (a) Number (b) Number (C) Number (d) Number (e) Number |Units Units Units () (9) Number | Units

Explanation / Answer

a) f = w / 2 pi = 4.3 / 2 pi = 0.684 Hz

b) lambda = v / f = 55.6 / 0.684 = 81.2 cm

c) ym = 6 cm

d) k x = 1.7

k = 1.7 / 0.22 = 7.73 N/m

e) w = 4.3 s-1

f) negative

g) v = sqrt [T / mu]

T = v2 * mu = 0.5562 * 0.43

T = 0.133 N

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