Question 530: Waves

Question

The frequency of a sonometer wire is $$100 \mathrm{~Hz}$$ When the weights producing the tensions are completely immersed in water, the frequence becomes $$60 \mathrm{~Hz}$$ and on immersing the weights in a certain liquid, the frequency becomes $$40 \mathrm{~Hz}$$. The specific gravity of the liquid is

Accepted Answer

As we know, frequency
$$f \propto \sqrt{m g} 	ext { or } f \propto \sqrt{g} \Rightarrow \frac{f_w}{f_{	ext {air }}}=\sqrt{\frac{g^{\prime}}{g}}$$
In water, $$f_w=0.6 f_{	ext {air }}, \frac{g^{\prime}}{g}=(0.6)^2=0.36$$
Let $$ho_w=$$ relative density of water
$$ho_m=$$ relative density of medium
$$ho_l=$$ relative density of liquid
$$\Rightarrow \quad 1-\frac{ho_w}{ho_m}=0.36 \Rightarrow \frac{ho_w}{ho_m}=0.64\quad 	ext{..... (i)}$$
In liquid, $$g^{\prime} / g=(0.4)^2=0.16$$
$$1-\frac{ho_l}{ho_m}=0.16 \Rightarrow \frac{ho_l}{ho_m}=0.84 \quad 	ext{..... (ii)}$$
from Eqs. (i) and (ii)
$$\frac{ho_l}{ho_m}=\frac{0.84}{0.64} \Rightarrow 1.31=ho_l$$

Answer

1.42

Answer

1.31

Answer

1.82

Answer

1.21

Waves

The frequency of a sonometer wire is $100 \mathrm{~Hz} When the weights producing the tensions are completely immersed in water, the frequence becomes 60 \mathrm{~Hz} and on immersing the weights in a certain liquid, the frequency becomes 40 \mathrm{~Hz}$. The specific gravity of the liquid is

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