A wire with mass 45.0g is stretched so that its ends are tied down at points a d

Question

A wire with mass 45.0g is stretched so that its ends are tied down at points a distance 75.0cm apart. The wire vibrates in its fundamental mode with frequency 60.0Hz and with an amplitude at the antinodes of 0.270cm .

What is the speed of propagation of transverse waves in the wire? ANS= 90 m/s

Compute the tension in the wire. ANS= 486 N

Find the magnitude of the maximum transverse velocity of particles in the wire. ????

Find the magnitude of the maximum acceleration of particles in the wire. ????

Explanation / Answer

infundamental mode the there will be a nodes at the ends

so L = ?/2 = 0.75 m

? = 2L = 1.5 m

frequency fo = 60 Hz

speed = ?*fo = 1.5*60 = 90 m/s

angular speed = w = 2*pi*f = 2*3.14*60 = 376.8 rad/s

the particles of the wire are in SHM

maximum transverse speed = Vmax = A*w = 0.0027*376.8 = 1.017 m/s

maximum acceleration amax = w^2*A = 376.8*376.8*0.0027 = 3.83*10^2 m/s^2

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