Question

A horizontal metal wire is fixed on a state of tension between two vertical supports when plucked it gives a fundamental frequency f_O.

1. Obtain a mathematical expression for f_O

2. A 5.5 m wire has a mass of 0.035 kg. If the tension of the string is 77N, the speed of wave on the string is

• 110 ms^-1
• 11\(\sqrt{10}\)ms^-1
• 77 ms^-1
• 11 ms^-1
• 102 ms^-1

3. What change, if any, will be observed in the fundamental frequency if the wire is now immersed in water and plucked again?

Answer 1

1. We know velocity on a string, V = \(\sqrt{T/m}\) 

But V = λf

2. Mass per unit length, m = Mℓ=0.0355.5

= 6.36 × 10^-3kg/m

T = 77N

3. Frequency does not change.