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Two waves A and B of frequencies 2MHz an...

Two waves A and B of frequencies 2MHz and 3 MHz, respectively are beamed in the same direction for communication via sky wave. Which one of these is likely to travel longer distance in the ionosphere before suffering total internal reflection?

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To determine which wave, A (2 MHz) or B (3 MHz), is likely to travel a longer distance in the ionosphere before suffering total internal reflection, we can analyze the relationship between frequency and the behavior of waves in the ionosphere. ### Step-by-Step Solution: 1. **Understanding the Concept of Total Internal Reflection**: - Total internal reflection occurs when a wave traveling from a medium of higher refractive index to a medium of lower refractive index hits the boundary at an angle greater than the critical angle. The critical angle is dependent on the refractive indices of the two media. 2. **Refractive Index and Frequency Relationship**: - The refractive index of the ionosphere increases with an increase in frequency. This means that higher frequency waves will experience a greater change in their speed and direction as they travel through the ionosphere. 3. **Analyzing the Given Frequencies**: - Wave A has a frequency of 2 MHz. - Wave B has a frequency of 3 MHz. - Since the refractive index increases with frequency, wave B (3 MHz) will have a higher refractive index compared to wave A (2 MHz). 4. **Effect on Angle of Refraction**: - Higher frequency waves (like wave B) will bend less when they encounter the ionosphere's boundary. This means that the angle of refraction will be smaller for wave B compared to wave A. 5. **Distance Traveled Before Total Internal Reflection**: - Because wave B (3 MHz) bends less and maintains a more direct path, it can travel a longer distance in the ionosphere before reaching the critical angle necessary for total internal reflection. In contrast, wave A (2 MHz) will bend more, potentially reaching the critical angle sooner. 6. **Conclusion**: - Therefore, wave B (3 MHz) is likely to travel a longer distance in the ionosphere before suffering total internal reflection compared to wave A (2 MHz). ### Final Answer: Wave B (3 MHz) is likely to travel longer distance in the ionosphere before suffering total internal reflection.
To determine which wave, A (2 MHz) or B (3 MHz), is likely to travel a longer distance in the ionosphere before suffering total internal reflection, we can analyze the relationship between frequency and the behavior of waves in the ionosphere. ### Step-by-Step Solution: 1. **Understanding the Concept of Total Internal Reflection**: - Total internal reflection occurs when a wave traveling from a medium of higher refractive index to a medium of lower refractive index hits the boundary at an angle greater than the critical angle. The critical angle is dependent on the refractive indices of the two media. 2. **Refractive Index and Frequency Relationship**: ...
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