The linear density of a string is 2x10-4 kg/m. A transverse wave on the string i

Question

The linear density of a string is 2x10-4 kg/m. A transverse wave on the string is described by the equation y = 0.02 sin [3.0mx + 12 where x and y are in meters and t is in seconds. Don't forget units. a. What is the amplitude? b. What is the wavelength? (0.667 m) c. What is the frequency? (6 Hz) d. What is the wave speed? (4 m/s) e. What is the tension in the string? (3.2x103 N) f. What is the maximum transverse speed of a particle in the string? 0.754 m/s g. How much time does it take for a particle in the string to move from y 1/50 m toy = 070.0417 s

Explanation / Answer

Given

y = 0.02*sin[3*pi*x + 12*pi*t]

= 2*10^-4 Kg/m

Comparing given equation with standard as

y = A*sin(kx - wt)

a) Amplitude = A = 0.02 m

b) Wavelength = 2pi/3pi = 2/3 = 0.667 m

c) Frequency = f = w/2pi = 12pi/2pi = 6 Hz

d) Wave speed = v = f*wavelength = 6*0.667 = 4 m/s

e) Tension = T = v^2* = 16*2*10^-4 = 3.2*10^-3 N

f) Maximum speed = Aw = 0.02*12pi = 0.754 m/s

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