A sinusoidal transverse wave is traveling along a string in the negative directi

Question

A sinusoidal transverse wave is traveling along a string in the negative direction of an x axis. The figure shows a plot of the displacement as a function of position at time t = 0; the y intercept is 4.0 cm. The string tension is 3.9 N, and its linear density is 32 g/m. Find the (a) amplitude, (b) wavelength, (c) wave speed, and (d)period of the wave. (e) Find the maximum transverse speed of a particle in the string.If the wave is of the form
y(x,t) = ym sin(kx - ?t + ?),
what are (f) k, (g) ?, and (h) ?, and (i) the correct choice of sign in front of ??

Explanation / Answer

(A)
From Figure it is Clear,
Amplitude, A = 4 cm

(B)
From Figure it is Clear,
Wavelength , = 40 cm

(C)
Wave speed is given by,
v = sqrt(F/u)
Where,
F is the Tension in the String, = 3.9 N
u = Mass per unit Length = 32 g/m = 0.032 Kg/m

v = sqrt(3.9 / 0.032)
v = 11.04 m/s
Wave speed, v = 11.04 m/s

(D)
We know,
v = f *
And f = 1/T
V = /T
T = /v
T = 0.40 / 11.04 s
T = 0.036 s

Period of the wave, T = 0.036 s

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