Transverse waves with a speed of 52.5 m/s are to be produced on a stretched stri

Question

Transverse waves with a speed of 52.5 m/s are to be produced on a stretched string. A 4.65-m length of string with a total mass of 0.0600 kg is used. What is the required tension in the string? Calculate the wave speed in the string if the tension is 8 00 N. The position of a 0.30-kg object attached to a spring is described by x = (0.25 m) cos(0.4. pi t) Find the amplitude of the motion. Find the spring constant. Find the position at t = 0.27 s. Find the object's speed at t = 0.27 s. A man enters a tall tower, needing to know its height. He notes that a long pendulum extends from the calling almost to the floor and that ns period is 21.5 s. How tall is the tower? If this pendulum is taken to the Moon, where the free-fall acceleration is 1.67 m/s^2, what is the period there?

Explanation / Answer

1)

a) from the given data

linear mass density of the string, mye = m/L

= 0.06/4.65

= 0.0129 kg/m

we know, wave speed, v = sqrt(T/mue)

==> T = v^2*mue

= 52.5^2*0.0129

= 35.6 N

b)

v = sqrt(T/mue)

= sqrt(8/0.0129)

= 24.9 m/s

2)

a) A = 0.25 m

b) k = m*w^2

= 0.3*(0.4*pi)^2

= 0.474 N/m

c) x = 0.25*cos(0.4*pi*0.27)

= 0.24 m

d) v = -0.25*0.4*pi*sin(0.4*pi*0.27)

= -0.10 m/s

3)

a) use, T = 2*pi*sqrt(L/g)

L = T^2*g/(4*pi^2)

= 21.5^2*9.8/(4*pi^2)

= 115 m

b) T = 2*pi*sqrt(L/g_moon)

= 2*pi*sqrt(115/1.67)

= 52.1 s

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