A standing wave pattern is observed in a thin wire with a length of3.00 m. The e

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 Hz

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