A fellow student with a mathematical bent tells you that the wave function of a

Question

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is

y(x,t) = 2.15 mm cos[(6.95rad/m)x + (748 rad/s)t].

Being more practical, you measure the rope to have a length of 1.60 m and a mass of 0.00338 kg. You are then asked to determine the following.

(a) amplitude

2.15mm

(b) frequency

118Hz

(c) wavelength

.904m

(d) wave speed

107.62 m/s

(e) direction the wave is traveling

x-direction    

(f) tension in the rope

N

(g) average power transmitted by the wave

W

Explanation / Answer

Hence mass per unit length µ = 0.00338 kg / 1.60 m = 2.1125 x 10-3 kg/m
(f) Tension in the string T = µ v2 = 2.1125 x 10-3 x (107.62)2 = 24.467 N

(g) Average Power is given by P = ½ x µ 2 A2 v = 0.5 x 2.1125 x 10-3 x 7482 x (2.15 x 10-3 )2 x 107.62 = 0.293 Watt

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