Question

A clamped 24 cm wire with 25 g/m mass density vibrates at its fundamental mode near an 85 cm long open/closed tube. The wire vibration excites the second harmonic of the tube. What is the tension in the wire in N?

Answer 1

Answer:

T = 518.4 N

Explanation:

Length of wire,l = 24 cm = 0.24 m

mass density of wire,μ = 25 g/m = 0.025 g/m

Length of the tube, L = 85 cm = 0.85 m

speed of sound, v = 340 m/s

frequency in the tube in open/closed tube

$f_{3} = \dfrac{3v}{4L}$

$f_{3} = \dfrac{3\times 340}{4\times 0.85}$

$f_{3} = 300\ Hz$

now, calculation of tension in the wire.

Frequency in the wire will be same as frequency in the tube

$f = \dfrac{v_{wire}}{2 l}$

$v_{wire} = \sqrt{\dfrac{T}{\mu}}$

now,

$f = \dfrac{1}{2 l}\times \sqrt{\dfrac{T}{\mu}}$

squaring both side and arranging

$T = f^2\times 4l^2 \times \mu$

$T = 300^2\times 4\times 0.24^2 \times 0.025$

     T = 518.4 N

hence, the tension in wire is equal to T = 518.4 N