A stretched string fixed at each end has a mass of 45.0 g and a length of 7.00 m. The tension in the string is 41.0 N. (a) Determine the positions of the nodes and antinodes for the third harmonic. (Enter your answers from smallest to largest distance from one end of the string.) nodes: 0 2.3 4.7 7 Ii It antinodes 1.15 3.55 5.85 In (b) What is the vibration frequency for this harmonic? 11.2X Your response differs from the correct answer by more than 10%. Double check your calculations. Hz
Solution
frequency f = V/L = sqrt(T/u)/L
here L/2 = 7/3
L = 4.67 m
u is mass per unit length
u = 0.045/7 = 0.0064 kg/m
V = sqrt(41/0.0064)
V = 80.03 m/s
so f = v/L = 80.03/(4.67)
f = 17.13 Hz
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let t1 and t2 be the two time intervals that are taken to make to anf fro.
so here t1 + t2 = 1.8
Distance y = (1/2)*g*t1^2
and Distance y = V*t2
(1/2)*g*t1^2 = V*t2
(1/2)*9.8*t1^2 = 343*(1.8-t1)
4.9*t1^2 = 617.4 - 343*t1
solving for t1,
t1 = 1.75 secs
h = (1/2)*g*t1^2
h = 0.5* 9.81 * 1.75^2
h = 15.02 m
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A stretched string fixed at each end has a mass of 45-0 g and a length.docx
1. A stretched string fixed at each end has a mass of 45.0 g and a length of 7.00 m. The tension in
the string is 41.0 N. (a) Determine the positions of the nodes and antinodes for the third
harmonic. (Enter your answers from smallest to largest distance from one end of the string.)
nodes: 0 2.3 4.7 7 Ii It antinodes 1.15 3.55 5.85 In (b) What is the vibration frequency for this
harmonic? 11.2X Your response differs from the correct answer by more than 10%. Double
check your calculations. Hz
Solution
frequency f = V/L = sqrt(T/u)/L
here L/2 = 7/3
L = 4.67 m
u is mass per unit length
u = 0.045/7 = 0.0064 kg/m
V = sqrt(41/0.0064)
V = 80.03 m/s
so f = v/L = 80.03/(4.67)
f = 17.13 Hz
----------------------------------------------------
let t1 and t2 be the two time intervals that are taken to make to anf fro.
so here t1 + t2 = 1.8
Distance y = (1/2)*g*t1^2
2. and Distance y = V*t2
(1/2)*g*t1^2 = V*t2
(1/2)*9.8*t1^2 = 343*(1.8-t1)
4.9*t1^2 = 617.4 - 343*t1
solving for t1,
t1 = 1.75 secs
h = (1/2)*g*t1^2
h = 0.5* 9.81 * 1.75^2
h = 15.02 m
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