4. A rope, under tension of 200 N and fixed at both ends, oscillates in a second harmonic standing wave pattern. The displacement of the rope is given by: πχ sin (12πt) y(x, t) = (0.10 m) (sin where x = 0 at one end of the rope, x is in meters, and t in seconds. What are: (a) the length of the rope, (b) the speed of the waves on the rope, and (c) the mass of the rope? (d) If the rope oscillates in a third harmonic standing wave pattern, what will be the period of oscillations?
4. A rope, under tension of 200 N and fixed at both ends, oscillates in a second harmonic standing wave pattern. The displacement of the rope is given by: πχ sin (12πt) y(x, t) = (0.10 m) (sin where x = 0 at one end of the rope, x is in meters, and t in seconds. What are: (a) the length of the rope, (b) the speed of the waves on the rope, and (c) the mass of the rope? (d) If the rope oscillates in a third harmonic standing wave pattern, what will be the period of oscillations?
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Transcribed Image Text:4. A rope, under tension of 200 N and fixed at both ends, oscillates in a second
harmonic standing wave pattern. The displacement of the rope is given by:
(sin 2) sin (12πt)
y(x, t) = (0.10 m) (sin
where x = 0 at one end of the rope, x is in meters, and t in seconds.
What are:
(a) the length of the rope,
(b) the speed of the waves on the rope, and
(c) the mass of the rope?
(d) If the rope oscillates in a third harmonic standing wave pattern,
what will be the period of oscillations?
Ans. 4 m; 24 m/s; 1.4 kg; 0.11
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