Resonance Questions

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:

The circuit shown below acts as:

What is the value of inductance $L$ for which the current is a maximum in a series $LCR$ circuit with $C=10\mu \text{F}$ and $\omega =1000{\text{s}}^{-1}$?

In the given circuit the reading of voltmeter $V_1$ and $V_2$ are $300\text{ volts}$ each. The reading of the voltmeter $V_3$ and ammeter $A$ are respectively:

In an electrical circuit $R,L,C$ and an a.c voltage source are all connected in series. When $L$ is removed, the phase difference is $\pi /3$. If instead $C$ is removed, the phase difference is again $\pi /3$. The power factor of the circuit is:

The condition under which a microwave oven heats up a food item containing water molecules most efficiently is:

A string is stretched between fixed points separated by $75.0\text{cm}$. It is observed to have resonant frequencies of $420\text{Hz}$ and $315\text{Hz}$. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is: