A radio receiver is tuned to 560 kHz, and its local oscillator frequency is 1,000 kHz. At the output, another signal is also received along with the desired signal. What is the frequency of the other station?

Explanation:

When a radio receiver is tuned to a specific frequency, it uses a local oscillator to convert the desired radio frequency signal to an intermediate frequency (IF) for easier processing. The frequency of the local oscillator is chosen such that the difference between the local oscillator frequency and the desired signal frequency equals the intermediate frequency.

Given:

• Tuned Frequency (f_signal): 560 kHz
• Local Oscillator Frequency (f_LO): 1,000 kHz

The intermediate frequency (IF) can be calculated using the formula:

IF = |f_LO - f_signal|

Substituting the given values:

IF = |1,000 kHz - 560 kHz| = 440 kHz

This means that the intermediate frequency is 440 kHz. However, due to the nature of the mixing process in the radio receiver, another signal can also produce the same intermediate frequency. This other signal will be at a frequency such that the absolute difference between its frequency and the local oscillator frequency also equals the intermediate frequency.

Let f_other be the frequency of the other signal. Then,

|f_LO - f_other| = IF

Substituting the values:

|1,000 kHz - f_other| = 440 kHz

Solving for f_other:

f_other = 1,000 kHz - 440 kHz = 560 kHz

or

f_other = 1,000 kHz + 440 kHz = 1,440 kHz

Since 560 kHz is the frequency of the desired signal, the other signal must be at 1,440 kHz.

Thus, the frequency of the other station is 1,440 kHz.