3. where x and y are in meters and t in seconds. If the linear (15 pts) The wave

Question

3. where x and y are in meters and t in seconds. If the linear (15 pts) The wave function for a wave on a taat string h yat)-0.350 sin (10-t Find the mass density of the string is 750 g/m, (a) (2 pts) amplitude, (b) (2 pts) wavelength, (c) (2 pts) wave speed (d) (2 pts) tension of the string (c) (3 pts) Find the maximum transverse speed of a particle in the string same direction along the same string with the phase angle of 0 ad relative to wave 1. What is te amplituef the resultant wave (exhibiting interference)? (0 (4 pts) Now suppose that another sinusoidal transverse wave with an amplitude of 35 cm is traveling in the

Explanation / Answer

y = A sin[ wt - k x + phi0]

and Given equation,

y = 0.350 sin(10 pi t - 3 pi x + pi/4 )

Comparing with so,

A = 0.350 m , w = 10 pi s^-1 , k = 3 pi m^-1 , phi0 = pi / 4 rad

(A) A = 0.350 m

(B) wavelength = 2 pi / k = 2/3 m

(C) wave speed , v = w / k = 10/3 m/s

(D) linear mass density = 0.075 kg/m

v = sqrt[ T / linear mass density]

(10/3)^2 = T / (0.075)

T = 0.833 N

(E) v_max = A w = (0.350) (10pi) = 11 m/s

(F) both are in phase.

so A = 0.350 + 0.350 = 0.700 m

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