Question

In a sonometer wire tension is maintained by suspending a 50.7 kg mass from the free and of the wire the suspended mass has a volume of 0.0075 metre cube then the fundamental frequency of the wire is it to 60 words with the suspended mass is completely submerged in water and the fundamental frequency will become ( take g as 10)​

Answer 1

Answer:

Fundamental Frequency in such a string is directly proportional to square root of tension.

ν  fundamental   =k  $\sqrt{T}$

​ν  fundamental  =c  $\sqrt{m}$

(c is constant of different value, we take out g from tension, T = mg)

i.e.

$\frac{260}{\sqrt{50.7}} }= constant$

Now the block is 0.0075 $m^{3}$ , by Archimedes principle we know that an upward buoyant force of ie;

ρVg=1000×0.0075×g=7.5g acts.

This is equivalent to the block losing 7.5 kg in mass.

i.e=50.7−7.5=43.2

Substituting this.

$\frac{260}{\sqrt{50.7}} }= \frac{v}{\sqrt{43.2} }$

Solving this we get ν=240 Hz ,which is the new fundamental frequency.