PHYSICS UNIVERSITY

DAMON

2013-11-18 6:53 am

A 1.80-m string of weight 0.0125N is tied to the ceiling at its upper end, and the lower end supports a weight W. Neglect the very small variation in tension along the length of the string that is produced by the weight of the string. When you pluck the string slightly, the waves traveling up the string obey the equation
y(x,t)=(8.50mm)cos(172rad/m(x) −2730rad/s ( t)) Assume that the tension of the string is constant and equal to W.

Part A

How much time does it take a pulse to travel the full length of the string?

Part B

What is the weight W?

part C
How many wavelengths are on the string at any instant of time?

回答 (1)

天同

2013-11-18 8:41 am

✔ 最佳答案

(A). Frequency of wave = 2730/(2.pi) Hz
Wavelength of wave = 2.pi/172 m
Hence, speed of wave = [2730/(2.pi)] x [2.pi/172] m/s = 15.87 m/s
Time taken for the wave to travel the full length of string
= 1.8/15.87 s = 0.1134 s

(B). Mass per unit length of the string
= (0.0125/g)/1.8 kg/m =6.944x10^-4 kg/m
where g is the acceleration due to gravity, taken to be 10 m/s^2

Hence, 15.87 = square-root[W/6.944x10^-4]
W = 15.87^2 x (6.944x10^-4) N = 0.1749 N

(C). No. of wavelengths = 1.8/(2.pi/172) = 49.27

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