A string is stretched between two ends with a tension of16 N. The linear mass de

Question

A string is stretched between two ends with a tension of16 N. The linear mass denisty of the string is 0.25kg/m. The left end of the string is given a simple harmonicmotiion with a frequency of 5 Hz and an amplitude of 3 cm such thatt = 0s, this end of the string has zero displacement and is movingin the positive y-direction. a) Write down the specific wave function for this wave. b) What is the wave speed and wavelength? c) Is the power transmitted by the oscillator in one periodthe same as that transmitted along the wave in onewavelength? d) If a standing wave with fundamental frequency of 50 Hz isto be created by this wave, what needs to be the legth of the wirebetween two ends? Thank you. A string is stretched between two ends with a tension of16 N. The linear mass denisty of the string is 0.25kg/m. The left end of the string is given a simple harmonicmotiion with a frequency of 5 Hz and an amplitude of 3 cm such thatt = 0s, this end of the string has zero displacement and is movingin the positive y-direction. a) Write down the specific wave function for this wave. b) What is the wave speed and wavelength? c) Is the power transmitted by the oscillator in one periodthe same as that transmitted along the wave in onewavelength? d) If a standing wave with fundamental frequency of 50 Hz isto be created by this wave, what needs to be the legth of the wirebetween two ends? Thank you.

Explanation / Answer

tension T = 16 N
The linear mass denisty of the string = 0.25kg/m frequency f = 5 Hz Amplitude A = 3 cm                    = 0.03 m   a)Specific wave function for this wave y = A sin (2f t )                                                             = (0.03 m ) sin ( 10t ) (b). wavespeed v = [ T / ]                            = 8 m / s wavelength = v / f                      =1.6 m (d). fundamental frequency F = 50 Hz we know F = ( 1/ 2L ) v from this length of the wire L = v / 2F                                             = 0.08 m

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