A wire with mass 40.0 g is stretched so that its ends are tied down at points 80.0 cm apart.The wire vibrates in its fundamental mode with frequency 60.0 Hz and with an amplitude at the antinodes of 0.300 cm.
(a) What is the speed of propagation of transverse wave in the wire?
Compute the tension in the wire.
(c) Find the maximum transverse velocity and acceleration of particles in the wire.

Answer

A, B, C, D

Explanation

(a)`lambda/2 = l` or `lambda= 2l = 1.6 m `
`v = f lambda = 60 xx 1.6 = 96 m//s`
`(b) v = sqrt(T/mu)`
`:. T = muv^2 = (0.04/0.8) (96)^2`
= 461 N
(c) `v_(max) = omega A_(max)`
` = (2pif) A_(max)`
` = (2pi)(60)(0.003)`
` = 1.13 m//s `
` a_(max) = omega^2 A_(max)`
` = (2pif)^2 A_(max)`
`=(2pi xx 60)^2 (0.003)`
`=426.4 m//s^2` .