A sinusoidal transverse wave is travelling along a string in the negative direct

Question

A sinusoidal transverse wave is travelling 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 2.7 N, and its linear density is 26 g/m. Find the (a) amplitude, (b) wavelength, (e) 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?

Explanation / Answer

(A) Amplitude = 5 cm = 0.05 m

(B) wavelength = 40 cm = 0.40 m

(C) v = sqrt[ T / linear density]

linear density = 26 x 10^-3 kg / m = 0.026 kg / m

v= sqrt[ 2.7 / 0.026] = 10.2 m/s

(d) priod of wave, T = wavelength / speed

= 0.40 / 10.2

= 0.0392 s

= 39.2 ms

(e) v_max = A w = 2 pi A / T = 2 x pi x 0.05 / 0.0392

= 8 m/s

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