A standing wave on a tight string experiment isset up in the laboratory. One end

Question

    A standing wave on a tight string experiment isset up in the laboratory. One end of the string is attachedto an oscillator that vibrates with a frequency of 60 Hz. Theother end of the string passes over a pulley and is attached to amass. The distance between the oscillator and the pulley is1.2 m. When the oscillator is turned on, six loops areobserved on the string. The linear mass density of the stringis 1.4 g/m.

a.     A. What is the wavelength of the standing wave?

b.     B.What is the wave speed of the standing wave?

c.       C. How much mass is hangingon the string?

Please Show ALL work and Formulasused to get the answer. Thank You!

    

Explanation / Answer

   a.   No. of completewavelengths onstring  n    =   6 /2   =   3          Wavelength      =   L/ n   =   1.2 m /3   =   0.40   m   =   40   cm    b.   Frequency   f   =   n* f0   =   3 *60   =   180   Hz          Wavevelocity   v   =   f *   =   180 *0.4   =   72.0   m/s    c.   Also   v   =   (T/m)    m   =   massper unit length   =   1.4g/m   =   1.4 *10-3   kg/m          T   =   v2* m   =   72.02 * 1.4 *10-3   =   7.26   N

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