Question

Consider the broadcasting circuit for an AM radio station which broadcasts at a frequency of 1330 kHz. The free electrons in such a circuit are moving back and forth in simple harmonic motion. (a) How long does it take for the free electrons in this circuit to go back and forth once? Give your answer in microseconds. .752 Correct: Your answer is correct. μs (b) Assuming the average speed of the free electrons is 100 μm/s, what is the range of motion of the electrons as they go back and forth in the wires of the circuit. (HINT: As a free electron goes back and forth, it travels its full range every half cycle.) Give your answer in nanometers. .0376 Correct: Your answer is correct. nm

Answer 1

Answer:

a) T = 0.752 μm

b) x = 0.0378 nm

Explanation:

a) In a simple harmonic motion the time that takes the electron to go back and forth once is given by the period in the circuit:

$T = \frac{1}{f}$

where T: is the period and f: is the frequency

$T = \frac{1}{1330\cdot 10^{3}s} = 0.752 \mu s$

b) The average speed of the electrons is the following:

$v = \frac{x}{T}$

where x: is the range of motion and T: is the period

Taking into account that the electron travels its full range every half cycle, that is to say, every T/2, the range of motion of the electrons is:

$x = v \cdot \frac{T}{2} = 100 \cdot 10^{-6}m/s \cdot \frac{0.752 \cdot 10^{-6}}{2}s = 0.0378 nm$

I hope it helps you!