A standing wave pattern is created on a string with mass density ? = 0.00031 kg/

Question

A standing wave pattern is created on a string with mass density ? = 0.00031 kg/m. A wave generator with frequency f = 68.0 Hz is attached to one end of the string and the other end goes over a pulley and is connected to a mass (ignore the weight of the string between the pulley and mass). The distance between the generator and pulley is L = 0.63 m. Initially the 3rd harmonic wave pattern is formed. Keeping the frequency fixed at f = 68.0 Hz, what is the maximum mass that can be used to still create a coherent standing wave pattern?

Explanation / Answer

velocity = squreroot (tension / unit length) , ..................(1) velocity = frequency x wave length . .........(2) for 1st harmonic or third harminc, velocity is same. fundamental frequency = 68 Hz wavelength = 2 * length = 2* 0.63 = 1.26 m based on 2nd equation , velocity = 68 Hz * 1.26m = 85.68 m /s lets make T as the subject in the first equation, tension = (unit length) x velocity ^2 T = 0.000031kg/m x 85.68 ^2 T= 0.2275 N tenstion T = mass x gravity mass (m) = tension (T) / (gravity (g) m = 0.2275 /9.81 m = 0.0231 kg

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