A string is connected to a motor that propagates a vibration on the string when

Question

A string is connected to a motor that propagates a vibration on the string when there is tension applied to the string. A sample of that string that is 1 m long has a mass of 25 g. If the string is pulled horizontally over a pulley and connected to a hanging mass of 350 g and the length of the string from motor to pulley is 0.75 m and there are 10.5 standing waves what is the frequency of oscillation of the motor? (a) Draw a diagram and label all parameters correctly (b) What is the label value for the string? (c) Find the frequency of oscillation (d) How much hanging mass would be needed to produce 4.5 standing waves? (e) If the mass per unit length was tripled how would the answers for parts c and d change?

Explanation / Answer

b) mass per unit length u = mass / length = 0.025 kg / 1 m = 0.025 kg /m

c) Tension, T = mg = 0.350 x 9.81 = 3.43 N

there are 10.5 standing waves in 0.75 m

wavelength = length of 2 standing waves = 2 ( 0.75 / 10.5)

         = 0.143 m

speed of wave = sqrt[T / linear mass density ] = sqrt[3.43 / 0.025] = 11.71 m/s

frequency = speed / wavelength = 11.71 / 0.143

      = 81.91 Hz

d) new wavelength = 2(0.75 / 4.5 ) = 0.333 m

then speed = wavelength x frquency = 0.333 x 81.91 = 27.30 m/s

27.30 = sqrt[ T / 0.025 ]

T = 18.64 N

m = T/9.81 = 1.90 kg

e) u = 3 x 0.025 = 0.075 kg /m

v = sqrt[ 3.43 / 0.075] = 6.76 m/s

f = v / lambda = 6.76 / 0.143 = 47.29 Hz

-----------------------------

speed = wavelength x frquency = 0.333 x 47.29 = 15.75 m/s

15.75 = sqrt[ T / 0.075 ]

T = 18.60 N

m = T/9.81 = 1.90 kg

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