The length and diameter of a metal wire used in sonometer is doubled. The fundamental frequency will change from 'n' to

An alternating e.m.f. is $$\mathrm{e}=\mathrm{e}_0 \sin \omega \mathrm{t}$$. In what time the e.m.f. will have half its maximum value, if '$$\mathrm{e}$$' starts from zero? ($$\mathrm{T}=$$ time period, $$\sin 30^{\circ}=0.5$$)

A ray of light is incident on one face of an equilateral glass prism having refractive index $$\sqrt{2}$$. It produces the emergent ray which just. grazes along the adjacent face. The value of angle of incidence is $$\left(\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right)$$

The input a.c. voltage of frequency $$60 \mathrm{~Hz}$$ is applied to half-wave rectifier and also to full-wave rectifier. The output frequency in case of half-wave rectifier and that in case of full wave rectifier is respectively.