AIIMS 2007 Physics Modulation MCQ Question

To solve the question regarding the number of stations that can be accommodated in a given bandwidth when considering the highest modulating frequency, we can follow these steps:

Explanation:

1. Understanding Modulation and Bandwidth:

   • In communication systems, modulation is the process of varying one or more properties of a carrier wave in accordance with a modulating signal. The highest modulating frequency determines how much bandwidth is required for the transmission.
   • According to the Nyquist criterion, the bandwidth required for a signal is twice the highest frequency of the modulating signal.

2. Calculating the Bandwidth Required for One Station:

   • Given that the highest modulating frequency $f_m$ is 5 kHz, the required bandwidth $B$ for one station can be calculated as: $B = 2 \cdot f_m = 2 \cdot 5 \text{ kHz} = 10 \text{ kHz}$

3. Determining the Total Bandwidth Available:

   • We have a total bandwidth of 150 kHz available for accommodating multiple stations.

4. Calculating the Number of Stations:

   • To find out how many stations can fit into this bandwidth, we divide the total bandwidth by the bandwidth required for one station: $N = \frac{\text{Total Bandwidth}}{\text{Bandwidth per Station}} = \frac{150 \text{ kHz}}{10 \text{ kHz}} = 15$

Conclusion:

Thus, the number of stations that can be accommodated in a 150 kHz bandwidth is 15. Therefore, the correct answer is A) 15.

Clarifying Other Options:

• B) 10: This option suggests that only 10 stations can fit, which is incorrect based on the calculations as we have determined that 15 stations can fit.
• C) 5: This option is also incorrect since it underestimates the number of stations that can be accommodated.
• D) None of these: This option is not valid because we have confirmed that option A is indeed the correct answer.

Summary of Key Points:

• Highest modulating frequency $f_m = 5$ kHz leads to a required bandwidth of $10$ kHz per station.
• With $150$ kHz total bandwidth, you can accommodate $15$ stations.
• Therefore, the correct answer is A) 15.