Ull a StPing (Fall 2015-2016) A string 0.9 m long with linear mass density u=2x10 kg/m is fixed at both T=10 N. A standing wave is generated along the string as shown in the figure. %3D (a) Find the speed of the wave on the string. (b) What is the harmonic of the standing wave, (n= ?) Deduce its wavelength. (c) Determine the location of the second antinode on the string. (d) What is the frequency of the string oscillation? (e) Write the equation of the standing wave shown on the figure below, y (x,t), wit meters and the time t in seconds. (f) At what times would all elements of the string of the standing wave have a zer Would the energy in the string be equal to zero at these instants? Justify. Solution:
Ull a StPing (Fall 2015-2016) A string 0.9 m long with linear mass density u=2x10 kg/m is fixed at both T=10 N. A standing wave is generated along the string as shown in the figure. %3D (a) Find the speed of the wave on the string. (b) What is the harmonic of the standing wave, (n= ?) Deduce its wavelength. (c) Determine the location of the second antinode on the string. (d) What is the frequency of the string oscillation? (e) Write the equation of the standing wave shown on the figure below, y (x,t), wit meters and the time t in seconds. (f) At what times would all elements of the string of the standing wave have a zer Would the energy in the string be equal to zero at these instants? Justify. Solution:
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Transcribed Image Text:14/6
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PHYS220
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Problems and Sample Exams
Standing Wave on a String (Fall 2015-2016)
SEP 18-4
Camplex 17/6 11oSuu
A string 0.9 m long with linear mass density u=2×10 kg/m is fixed at both ends under a tension
T=10 N. A standing wave is generated along the string as shown in the figure.
(a) Find the speed of the wave on the string.
(b) What is the harmonic of the standing wave, (n= ?) Deduce its wavelength.
(c) Determine the location of the second antinode on the string.
(d) What is the frequency of the string oscillation?
(e) Write the equation of the standing wave shown on the figure below, y (x,t), with keeping x, and y in
meters and the time t in seconds.
(f) At what times would all elements of the string of the standing wave have a zero displacement, y = 0?
Would the energy in the string be equal to zero at these instants? Justify.
Solution:
0.2 m
(a) The speed on the string is:
T
2x10-3
10
=50 /2 =70.71m/s.
V= |-=
v = 70.71 m/s
- 0.2 m
L=0.9 m
(b) In the graph we have three loops on a string fixed at two ends so the resonance is in the 3rd harmonic,
n = 3.
n = 3rd harmonic
dNN = 0.3 m
By observation the string length has three loops so its length is:
L=34NN =0.9m=d=0.3m
2= 0.6 m
→%=D2×4NN3D2 ×0.3=0.6m.
Every loop has a length of dN
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