Answer :
To find the wavelength of the electromagnetic wave emitted by an LC oscillator, first calculate the resonant frequency using the formula for LC oscillation, then use the speed of light to find the wavelength from the frequency.
The question concerns determining the wavelength of an electromagnetic wave emitted by an LC oscillator circuit. The self-inductance (L) is given as 0.277 \\mu H\ and the capacitance (C) is 35.9 pF. To find the wavelength, we must first calculate the resonant frequency (f) of the oscillator using the formula \( f = \frac{1}{2\pi\sqrt{LC}} \), and then use the relationship between wavelength (\( \lambda \)), frequency (f), and the speed of light (c), which is \( \lambda = \frac{c}{f} \).
Let's proceed with the calculation steps:
Calculate the resonant frequency (f): \( f = \frac{1}{2\pi\sqrt{0.277 \\times\ 10^{-6} H \times 35.9 \\times\ 10^{-12} F}} \).
Once we have the frequency, calculate the wavelength (\( \lambda \)) using \( \lambda = \frac{c}{f} \), where c is the speed of light (\approx 3 \times 10^8 m/s).
This will provide us with the wavelength of the electromagnetic wave emitted by the LC oscillator.