A sinusoidal wave is traveling on a string with speed 17.50 cm/s. The displaceme

Question

A sinusoidal wave is traveling on a string with speed 17.50 cm/s. The displacement of the particles of the string at x = 15 cm is found to vary with time according to the equation y(x, t)= (5.0 cm) sin[6 - (7.0 s-1)t]. The linear density of the string is 8.0 g/cm.

(a) What is the frequency of the wave?
Hz

(b) What is the wavelength of the wave?
cm

(c) Give the general equation giving the transverse displacement of the particles of the string as a function of position and time. (Use x and t as appropriate wherex is in cm and t is in s.)
y(x, t) =

(d) Calculate the tension in the string.
N

Explanation / Answer

w = 7
so

f = 7/(2*pi)=1.114 Hz

b)

v = lambda f

lambda = .175/1.114=0.157 m=15.7 cm


c) so k = 2 pi/lambda = 2*pi/(15.7)=0.4

so y = 5 * sin(0.4 x - 7 t)

d)

v = sqrt(T/(u))

T = u v^2 = 8*100/1000 * .175^2=0.0245 N

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