A sinusoidal alternating voltage has a root-mean-square (r.m.s.) potential difference (p.d.) of $4.2\,\text{V}$ and a frequency of $50\,\text{kHz}$. This alternating voltage is connected across a resistor of resistance $760\,\Omega$. By using the peak voltage, show that the largest power dissipated by the resistor is $46\,\text{mW}$.
On Fig. 7.1, draw a smooth curve to show how the power $P$ dissipated in the resistor varies with time $t$ between $t = 0$ and $t = 40\,\mu\text{s}$. Take $P = 0$ at $t = 0$.
Use your line in (a)(ii) to explain how it shows that the mean power dissipated in the resistor is $23\,\text{mW}$.
The alternating voltage in (a) is now applied to a piezoelectric crystal in air. Explain the effect on the air surrounding the crystal.
A second piezoelectric crystal is placed in the air close to the first crystal. Explain what the surrounding air in (b)(i) does to the second crystal.