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 4.8 N, and its linear density is 34 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) = y_m sin (kx - omega t + phi), what are (f) k, (g) omega, and (h) phi, and (i) the correct choice of sign in front of omega? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units (g) Number Units (h) Number Units

Explanation / Answer

A) Amplitude :
The amplitude of the sinusoidal transverse wave is the maximum elongation from the x axis:
A = 5 cm

B) Wavelength :
and its wavelength is the distance between two consecutive maxima

lambda = 4*10 = 40 cm

C) wave speed :

Wave Speed = Sqrt(T/mu)

Wave speed = sqrt(4.8/0.034) = 11.882 m/s

D) Period of the wave :

T = 1/f
we know
f = v/lambda

T = lambda/v = 0.4/11.882 = 0.03366 sec

Please post separate question for the other parts.

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