In the equation for a stationary wave given by $y=5 \cos \frac{\pi x}{25} \sin 100 \pi t$. Here, $x$ is in cm and $t$ in second. A node will not occur at distance $x$ is equal to

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

A person is standing at some point between two parallel cliffs (not exactly at the centre). He claps, and hears two echoes: the first after $$1 \mathrm{~s}$$ and the second after $$2 \mathrm{~s}$$. If the speed of sound in air is $$330 \mathrm{~m} / \mathrm{s}$$, the distance between the two cliffs is