A transverse sinusoidal wave is generated at one end of a long, horizontal strin

Question

A transverse sinusoidal wave is generated at one end of a long, horizontal string by a bar that moves up and down through a distance of 1.00 cm. The motion is continuous and is repeated regularly 140 times per second. The string has linear density 145 g/m and is kept under a tension of 60.0 N.

(a) Find the maximum value of the transverse speed u. cm/s

(b) Find the maximum value of the transverse component of the tension. N

(c) What is the transverse displacement y of the string at these phases?cm

(d) What is the maximum rate of energy transfer along the string? W

(e) What is the transverse displacement y when this maximum transfer occurs? m

(f) What is the minimum rate of energy transfer along the string? W

(g) What is the transverse displacement y when this minimum transfer occurs? cm

Explanation / Answer

a) y = A cos (wt + phi)

A = 0.5 cm = 0.005 m, w = 2 pi f = 2 pi * 140 = 879.6 rad/s

Aw = 0.005 * 879.6 = 4.398 m/s

d) v= sqrt[F/mu] = 20.34 m/s

k = w/v = 879.6/ 20.34 = 43.2 rad/m

Rate of energy transfer = Fx A2 k w = 60 * 0.0052 * 43.2 * 879.6 = 57 W

e) Displacement y is zero

f) zero

g) The minimum transfer occurs at phases of n * pi

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