Consider the broadcasting circuit for an AM radio station which broadcasts at a
ID: 1511180 • Letter: C
Question
Consider the broadcasting circuit for an AM radio station which broadcasts at a frequency of 1400 kHZ. The free electrons in such a circuit are moving back and forth in simple harmonic motion. Assuming the average speed of the electrons is 100 um/s, what is the range of motion of the electrons as they go back and forth in the wires of the circuit. (hint: this is two part problem; first find the time for an electron to go back and forth once; then as it travels its full range every half cycle) Part II: what is the wavelength of the elctromagnetic radio waves emitted by this broadcsting circuit?
Explanation / Answer
i)
given
frequency, f = 1400 kHz = 1.4*10^6 hz
average speed, v_avg = 100 micro m/s = 1*10^-4 m/s
time period, T = 1/f
= 1/(1.4*10^6)
= 7.14*10^-7 s
range of electron = v_avg*T/2
= 1.4*10^6*(7.14*10^-7/2)
= 0.5 m
ii) apply, c = lamda*f
lamda = c/f
= 3*10^8/(1.4*10^6)
= 214.2 m