The displacement from equilibrium of each point on a string carrying a harmonic

Question

The displacement from equilibrium of each point on a string carrying a harmonic wave is given as a function of time and position on the string as y = (0.31 mm)cos((2 pi/lambda)x - (400 pi s^-1)t). If the wave travels along the string at a speed of 4.55 m/s, what is its wavelength? The displacement from equilibrium of each point on a string carrying a harmonic wave is given as a function of time and position on the string as y = (0.31 mm) cos((400 pi m^-1)x - (2 pi/T)t). If the wave travels along the string speed of 4.55 m/s, what is its period? The displacement from equilibrium of each point on a string carrying a harmonic wave is given as a function of time and position on the string as y = (0.31 mm)cos ((200 pi m^-1)x - (2000 pi s^-1)t). Calculate the speed of the wave. The displacement from equilibrium of each point on a string carrying a harmonic wave is given as a function of time and position on the string as y = (0.31 mm)cos((3 pi m^-1)x - (400 pi s^-1)t). The string is under a tension of 150 N. What is its linear mass density?

Explanation / Answer

a) = V T

w= 2pi/ T = 400 pi

T = 2/100 = 0.02 sec

= 4.55 ( 0,.02) = 0.091 m apprx

b) 2pi/ = 400 pi

= 0.005

T = / V = 0.005 / 4,55 = 1.25 x 10^ -5 sec apprx

c) 2pi / = 200 pi

= 0.01 m

2pi/ T = 2000 pi

T = 0.001 sec

V = 0.01/ 0.001 = 10 m/s

d) linear mass density = T / v^2

2pi/ = 3 pi, = 0.66 m apprx

2pi/ T = 400 pi

T = 0.005 sec

V = 0.66 / 0.005 = 132c m/s

Linear mass density = 150 / 132^2= 8.6 x 10^ -3 kg/ m

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