Question

Transverse pulses travel with a speed of 200 m/s along a taut copper wire whose diameter is 1.50 mm. (a) What is the tension in the wire? (The density of copper is 8.92 g/cm3 .) (b) If the wire is 0.45 m in length, what is the resonance frequency? (c) If there is an anti-node 0.075 m from the end, which harmonic is being excited.

Answer 1

a)

given

v = 200 m/s

d = 1.5 mm = 1.5*10^-3 m

we know, volume disnity of copper, rho = 8920 kg/m^3

linear mass density of copper, mue = rho*cross sectional area

= rho*(pi*d^2/4)

= 8920*(pi*0.0015^2/4)

= 0.0158 kg/m

we know, v = sqrt(T/mue)

==> T = v^2*mue

= 200^2*0.0158

= 633 N

b) use, v = lamda*f

f = v/lamda

= v/(2*L)

= 200/(2*0.45)

= 222 hz

c) lamda/4 = 0.075

==> lamda = 4*0.075

lamda = 0.3 m

we know, lamda = 2*L/n

==> n = 2*L/lamda

= 2*0.45/0.3

= 3rd harmonic