A string of length 1.50 m and of weight 0.012 5 N is stretched under constant te

Question

A string of length 1.50 m and of weight 0.012 5 N is stretched under constant tension along the x-axis of a chosen coordinate system. The string is slightly plucked so that a transverse wave is made to travel along the string, as described by the èxpression (x, t) = (8.50 mm)cos(172 ml x-48.3 s.] t (a) How much time is required for a pulse to travel through the full length of the string? (b) What is the tension in the string? e How many wave lengths of the traveling wave are on th e string at any instan of timei (d) At what frequency does a point on the string oscillate as the wave passes? (e) Please state a time, ineconds, at which the point at the center bf the string

Explanation / Answer

y = (8.50 mm) cos(172x - 48.3t)

y = A cos(k x - w t)

(A) v = w / k = 48.3 / 172 = 0.28 m/s

t = 1.50 / v =5.34 sec

(B) v = sqrt[ T / u]

u = linear mass density = (0.0125/9.81)/(1.50)

= 8.495 x 10^-4 kg/m

T = 6.66 x 10^-5 N

(c) wavelength = 2 pi / k = 0.0365 m

n = 1.50 / 0.0365 = 41

(d) f = w / 2pi = 7.7 Hz

(e) v = dy/dt = (8.50 x 48.3) sin(172x - 48.3t)

x = 1.50 / 2 = 0.75 m

172 x 0.75 = 48.3 t

t = 2.67 sec

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