A 1.6 meter string of weight 1.21 N is tied to the ceiling at its upper end, and

Question

A 1.6 meter string of weight 1.21 N is tied to the ceiling at its upper end, and the lower end supports a weight W. When you pluck the string slightly, the waves traveling up the string obey the equation y(x,t) = (8.5 mm)*cos(172 rad*m^-1 x - 2730rad*s^-1t)
A) how much time does it take a pulse to travel the full length of the string?
B) what is the weight W?

A 1.6 meter string of weight 1.21 N is tied to the ceiling at its upper end, and the lower end supports a weight W. When you pluck the string slightly, the waves traveling up the string obey the equation y(x,t) = (8.5 mm)*cos(172 rad*m^-1 x - 2730rad*s^-1t)
A) how much time does it take a pulse to travel the full length of the string?
B) what is the weight W?


A) how much time does it take a pulse to travel the full length of the string?
B) what is the weight W?

Explanation / Answer

t = d/v where d = 1.6 m is the length of the string and v is the velocity of the wave traveling up the string

v = ?/k = (1/2730) / (1/172) = 0.063 m/s

t = (1.6) / (0.063) = 25.4 seconds

(2) v = sqrt(T/?), where T is the tension in the string and ? is the linear mass density of the string

Here the tension in the string is created by the weight W, thus T = W, and ? = m/L, where m is the mass of the string and L is its length. Therefore,

v = sqrt(WL/m)

W = mv

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