9. A clothesline has a linear mass density of 0.28 kg/m, and is stretched with a
ID: 2013759 • Letter: 9
Question
9. A clothesline has a linear mass density of 0.28 kg/m, and is stretched with a tension T = 30 N. One end is given a sinusoidal motion with a frequency of 5.0 Hz and amplitude of 0.010 m. At the time t = 0 the end has zero displacement and is moving in the positive direction.(a) Find the wave speed, the amplitude, the frequency, period, wavelength, and the wave
number, of the wave motion.
(b) Write a wave function describing the wave.
(c) Find the position of the point at x = 0.25 m at time t = 0.10 sec.
Explanation / Answer
Given Linear mass density , = 0.28 kg / m Tension in the string , T = 30 N Frequency , f = 5.0 Hz Amplitude , A = 0.010 m a) Wave speed , v = T / v = 30 N / (0.28 kg / m) = 10.35 m/s Amplitude , A = 0.010 m Frequency , f = 5.0 Hz Period, T = 1/f = 0.2 s Wavelength , = v / f = 10.35 m/s / 5.0 Hz = 2.07 m Wave number , k = 2 / = 2 *3.14 / 2.07 m k = 3.033 rad /m b) y (x, t ) = A sin (kx - t ) Angular frequency , = 2 / T = 2 *3.14 / 0.2 s = 31.4 rad/s y (x, t ) = 0.01 m sin (3.033 x - 31.4 t) is the wave function c) Position at x = 0.25 m , t = 0.10 s Taking the wavefunction in part b and plug in the values y (0.25, 0.10s) = 0.01 sin (3.033 *0.25 m -31.4 *0.10 s) = 6.79 *10^-4 mRelated Questions
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