Derive an expression for the apparent frequencies when the medium of source is at rest, observer in motion.

What is Doppler's effect? Derive an expression for the apparent frequencies when the medium at source is in motion, observe at rest.

Derive an expression for resonant frequency.

Derive an expression for the apparent frequencies when source and observer moving in the same direction.

Derive an expression for the equivalent capacitance when capacitors are connected in parallel.

Derive an expression for the distance covered by the body during nth second of its motion.

Obtain an expression for the efficiency of an engine in terms of heat derived from source and heat rejected to the sink.

An a.c. source of e.m.f. epsilon = epsilon_0 sin omegat is connected in series with a pure resistance R only. Derive an expression for the instantaneous power of this circuit and show that it is pulsating in nature.