Question

A mass m is attached to the free end of a sonometer wire. The fundamental frequency of the
wire is found to be 500 cycles/sec when the mass is in air. It becomes 140 cycles/sec when
the mass is completely immersed in a liquid and 460 cycles/sec when the mass is completely
immersed in water. The specific gravity of the liquid is--- (Assume modes of vibrating string is
fundamental)​

Answer 1

Answer:

Answer

mass=m (in air)

f

1

=500cycles/s (in air)

Specific gravity=1

Specific gravity of the liquid=?

f

2

=8480cycles/sec

f

3

=460cycles/sec

Specific heat=f

1

f

3

f

2

Answer 2

Answer:

The specific gravity of the liquid is  2146.78

Explanation:

Step 1: The ratio of a substance's density to the density of a certain reference material is known as its relative density or specific gravity. For gases, the reference is air at room temperature, whereas liquids are almost generally measured in relation to the densest possible form of water.

$\text { mass }=\mathrm{m} \text { (in air) }$

$\mathrm{f}_1=500$ cycles$/ \mathrm{s}$ (in air)

Specific gravity =1

Step 2: Specific gravity of the liquid=?

$\mathrm{f}_2=8480$ cycles $/ \mathrm{sec}$

$\mathrm{f}_3=460$ cycles $/ \mathrm{sec}$

Specific heat $=f_1 \sqrt{\frac{f_2}{f_3}}$

Putting all values in above equation we get:

Specific heat= 2146.78728

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