A sinusoidal wave A sinusoidal wave is traveling on a string with velocity 40 cm
ID: 1403067 • Letter: A
Question
A sinusoidal wave A sinusoidal wave is traveling on a string with velocity 40 cm/s. The displacement of the particles of the sting at x = 10 cm is found to vary with time according to the equation, y(1 0cm.) = 5.0cm sinfl .0-(4.0s-1 )/] 5.0cm sin[1.0-(4.0s) The linear density of the string is 4.0 grams/cm. What are (a) the frequency and wavelength of the wave? (c) Write the general equation giving the transverse displacement of the particles of the string as a function of position and time. (d) Calculate the tension in the string. Present your problem solving process in a clear and understandable fashion and state your assumptions for full credit. (Worth 20 points) (b)Explanation / Answer
a) 2pif =4
f = 0.637 Hz
b) Wavelength = velocity / f
= 40 / 0.637 = 62.83 cm
c) k = 2pi / lamnda
k = 2pi / 62.83 = 0.1
y(x,t) = A sin(kx - wt)
y(x,t) = 5 cm sin[0.1x - 4t]
d) v = sqrt(T / linear density)
linear density = 4 x 10^-3 kg / 10^-2 m
= 0.4 kg/m
0.40 = sqrt( T / 0.4)
T = 0.064 N