Introduction:
A super-heterodyne receiver is a type of radio receiver that uses frequency mixing to convert the received signal to a fixed intermediate frequency (IF) for easier processing. The IF frequency is typically chosen to be lower than the received signal frequency for better selectivity and sensitivity. In this question, the IF of the receiver is given as 456 kHz and the received signal frequency is 1 MHz.

Explanation:
To understand why the image signal is within the medium band, we need to consider the concept of frequency mixing in a super-heterodyne receiver.

Frequency Mixing:
Frequency mixing is the process of combining two input frequencies to produce sum and difference frequencies. In a super-heterodyne receiver, the received signal frequency is mixed with the local oscillator (LO) frequency to produce the sum and difference frequencies. The sum frequency is typically filtered out, and the difference frequency is amplified and processed.

Image Frequency:
In a super-heterodyne receiver, there is a phenomenon called the image frequency. The image frequency is a frequency that is symmetrically located around the LO frequency with respect to the IF frequency. It is given by the equation:

Image Frequency = 2 * LO Frequency - Received Signal Frequency

If the image frequency falls within the frequency range of interest (medium band in this case), it can interfere with the desired signal and cause distortion.

Analysis:
In this question, the received signal frequency is given as 1 MHz and the IF is given as 456 kHz. To determine the image frequency, we can substitute these values into the equation:

Image Frequency = 2 * LO Frequency - 1 MHz

Since the image frequency needs to be within the medium band, it should be less than the IF frequency (456 kHz). Let's assume the LO frequency is f_LO.

456 kHz > 2 * f_LO - 1 MHz

Rearranging the equation, we have:

2 * f_LO < 1="" mhz="" +="" 456="" />
2 * f_LO < 1.456="" />
f_LO < 0.728="" />

Therefore, the LO frequency should be less than 0.728 MHz to ensure that the image frequency falls within the medium band.

Conclusion:
Based on the analysis, we can conclude that the image signal is within the medium band because the LO frequency (which determines the image frequency) is less than 0.728 MHz.