A 1.30-m string of weight 0.0128 N is tied to the ceiling at its upper end, and

Question

A 1.30-m string of weight 0.0128 N 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) = (8.50 mm) cos (172 rad middot m^-1 x -2730 rad middot s^-1 t) Assume that the tension of the string is constant and equal to W. 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?

Explanation / Answer

Here,

y = A * cos(k * x - w* t )

y = 8.5 mm * cos(172 rad/m - 2730 rad/s * t)

speed of wave = w/k

speed of wave = 2730/172 m/s

speed of wave = 15.87 m/s

time taken for pulse to travel = length/speed

time taken for pulse to travel = 1.30/15.87 s

time taken for pulse to travel = 0.0819 s

the time taken for pulse to travel is 0.0819 s

part B)

as v = sqrt(T/(m/L))

15.87 = sqrt(W * 1.30 * 9.8/0.0128)

solving for W

W = 0.253 N

the weight W is 0.253 N

part c)

wavelength of wave = 2pi/(172) m

wavelength of wave = 0.0365 m

number of wavelength on string = 1.30/0.0365

number of wavelength on string = 35.6

the number of wavelength on string at one instant is 35.6

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