Question

What is the weight W?

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

Constants A 1.50-m string of weight 0.0130 N is tied to the ceiling at its upper end, and the lower end supports a weight W. Neglect the very small varlation 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 v(z,t) (8.50 mm)cos (172 rad .m-2730 rad s1t) Assume that the tension of the string is constant and equai to W Part A How much time does it take a pulse to travel the full length of the string? t 9.45x102 s Previous Answers Correct ▼ Part B What is the welght W? W- .70

Answer 1

Given that, A string length (l) = 1.50 m and weight (w_s) = 0.0130 N y(x, t) = (8.50 mm) cos (172 rad m^-1 x - 2730 rad s^-1 t). Amplitude of the wave A = 8.50 mm. Wave number, K = 172 m^-1 And, Angular frequency, w = 2730 therefore The mass of the string m_s = w_s/g = 0.0130/9.8 m/s^2 m_s = 1.3265 times 10^-3 kg. And, Mass per unit length of the string of length is mu = m_s/L = 1.3265 times 10^-3/1.50 mu = 8.843 times 10^-4 kg/m \r\n How much time does it take a pulse to travel the full length of string? The wave speed V = w/k w = 2730 s^-1, k = 172 m^-1 v = 2730/172 = 15.87 m/s therefore wave speed = 15.87 m\s where, The speed of wave (v) to travel a distance of 'L' in time 't' sec v = L/t t = L/v = 1.50 m/15.87 m\s = 0.0945 s therefore The time taken by a pulse to travel the full length of string is t = 0.0945 s.