** One end of a string with a linear mass density of 7.60 X 10^-4 kg/m is connec
ID: 1393256 • Letter: #
Question
** One end of a string with a linear mass density of 7.60 X 10^-4 kg/m is connected to an oscillator with a frequency of 50.0 Hz. The other end is connected to a hanging variable mass, as shown in Figure 14-72. The string passes over a pulley, and the string between the oscillator and the pulley can vibrate freely. (a) The length of the vibrating section of the string is 0.500 m. What mass must be attached so that the string vibrates with (i) one antinode between the pulley and the oscillator and (ii) three antinodes between the pulley and the oscillator? (b) What is the oscillation frequency of the string in each case in part (a)?Explanation / Answer
a)
i)
m = linear mas density = 7.6 x 10-4 kg/m
f = 50
L = length = 0.5 m
M = mass hanging
T = Mg
Using the formula ::
f = (1/2L) sqrt (T/m)
f = (1/2L) sqrt (Mg/m)
50 = (1/(2 x 0.5) sqrt (M(9.8) /(7.6 x 10-4 ))
M = 0.194 kg
ii)
frequency of vibration , f' = 3 f= 3 x 50 = 150
Using the formula ::
f = (1/2L) sqrt (T/m)
f = (1/2L) sqrt (Mg/m)
150 = (1/(2 x 0.5) sqrt (M(9.8) /(7.6 x 10-4 ))
M = 1.745 kg
b) i) f = 50 Hz
ii) 150 Hz
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