A standing wave pattern is observed in a thin wire with a length of3.00 m. The e
ID: 1744383 • Letter: A
Question
A standing wave pattern is observed in a thin wire with a length of3.00 m. The equation of the wave isgiven below where x is in meters and t is inseconds. y = (0.006 m) sin (x) cos(100t) (a) How many loops does this patternexhibit?1
(b) What is the fundamental frequency of vibration of the wire?
2 Hz
(c) If the original frequency is held constant and the tension inthe wire is increased by a factor of 9, how many loops are presentin the new pattern?
3 y = (0.006 m) sin (x) cos(100t) (a) How many loops does this patternexhibit?
1
(b) What is the fundamental frequency of vibration of the wire?
2 Hz
(c) If the original frequency is held constant and the tension inthe wire is increased by a factor of 9, how many loops are presentin the new pattern?
3
Explanation / Answer
a) Length (L) of the thin wire = 3.0 m The equation of the wave is given below where x is inmeters and t is in seconds. y = (0.006 m) sin(x) cos (100t) This equation is compared with y =ymaxsin(kx)cos(t) In the standing wave pattern we know theformula for the wavelength is = 2L / n Here 'n' is the number of loops. And k = 2 / = =2.0 m Therefore = 2L / n n = 2L / = 2(3.0m) / (2.0m) = 3 b) We have = 2.0 m = 100 Then fundamental frequency is f = / 2 = (100) / (2) = 50 Hz y = (0.006 m) sin(x) cos (100t) This equation is compared with y =ymaxsin(kx)cos(t) In the standing wave pattern we know theformula for the wavelength is = 2L / n Here 'n' is the number of loops. And k = 2 / = =2.0 m Therefore = 2L / n n = 2L / = 2(3.0m) / (2.0m) = 3 b) We have = 2.0 m = 100 Then fundamental frequency is f = / 2 = (100) / (2) = 50 HzRelated Questions
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