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Chapter 10: Problem 1440

If two antinodes and three nodes are formed in a distance of \(1.21 \AA\), then the wavelength of the stationary wave is (A) \(2.42 \AA\) (B) \(6.05 \AA\) (C) \(3.63 \AA\) (D) \(1.21 \AA\)

Short Answer

Expert verified
The wavelength of the stationary wave is 1.21 Å, which corresponds to option (D). So, the correct answer is (D) \(1.21 \AA\).

Step by step solution

01

Determine the segments between nodes and antinodes

The given information states that there are two antinodes and three nodes within a distance of 1.21 Å. In a stationary wave, an antinode is formed between every pair of adjacent nodes. Therefore, there are two segments between nodes and antinodes. Each of these segments is half a wavelength long.
02

Calculate the total wavelength

Since we have two segments that are each half a wavelength long, their total length will be equal to one complete wavelength. The total length of these segments is given as 1.21 Å. Therefore, the wavelength of the stationary wave is 1.21 Å.
03

Identify the correct answer

The wavelength of the stationary wave is 1.21 Å, which corresponds to option (D). So, the correct answer is (D) \(1.21 \AA\).

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