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Chapter 20: Problem 2670

What should be the minimum length of the antenna capable of emitting audio signal of wave length \(\lambda ?\) (A) \((\lambda 4)\) (B) \((N 8)\) (C) \(\lambda\) (D) \((\lambda 2)\)

Short Answer

Expert verified
The minimum length of the antenna capable of emitting audio signal of wavelength \(\lambda\) should be \((\lambda / 4)\).

Step by step solution

01

Understand the relationship between antenna length and wavelength

The length of the antenna is directly related to the wavelength of the signal it can emit. For efficient transmission and reception of signals, the length of the antenna should be a multiple of the smallest possible fraction of the wavelength, which is a quarter-wavelength (\( \lambda / 4\)).
02

Evaluate each option

(A) \((\lambda / 4)\): This option represents the quarter-wavelength, which is the minimum length for efficient signal transmission. (B) \((N / 8)\): This option is not related to the wavelength. Hence, it is not a valid answer. (C) \(\lambda\): This option represents the full wavelength. Although an antenna of this length will work, it is not the minimum length required for efficient signal transmission. (D) \((\lambda / 2)\): This option represents the half-wavelength. As with the full wavelength, an antenna of this length will work, but it is not the minimum length required.
03

Choose the correct answer

Based on the above analysis, the correct answer is option (A) \((\lambda / 4)\), as it represents the minimum length of the antenna required for efficient signal transmission of a given wavelength.

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