Question

5. A piece of wire 50 cm long is stretched by a load of 2.5 kg and has a mass of 1.44 gm.
Find the frequency of the second harmonic.

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Answer 1

Given info : A piece of wire 50 cm long is stretched by a load of 2.5 kg and has a mass of 1.44 gm.

To find : The frequency of the second harmonic is..

solution : length of wire, l = 50cm = 0.5 m

the wire is stretched by load, T = 2.5 kgf = 25 N [ g = 10 m/s² ]

mass of the wire, m = 1.44 gm

linear mass density, μ = mass of wire/length of wire = 1.44 × 10¯³/0.5 = 2.88 × 10¯³ kg/m

using formula,

f = 2n₁

= 2 × 1/2l √(T/μ)

= 1/l √(T/μ)

now, f = 1/0.5 √(25/2.88 × 10¯³)

= √(25000/2.88)

= 186.34 Hz

Therefore the frequency of second harmonic is 186.34 Hz.