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Chapter 10: Problem 1442

If two almost identical waves having frequencies \(\mathrm{n}_{1}\) and \(\mathrm{n}_{2}\), produced one after the other superposes then the time interval to obtain a beat of maximum intensity is \(\ldots \ldots \ldots .\) (A) \(\left\\{1 /\left(\mathrm{n}_{1}-\mathrm{n}_{2}\right)\right\\}\) (B) \(\left(1 / \mathrm{n}_{1}\right)-\left(1 / \mathrm{n}_{2}\right)\) (C) \(\left(1 / \mathrm{n}_{1}\right)+\left(1 / \mathrm{n}_{2}\right)\) (D) \(\left\\{1 /\left(\mathrm{n}_{1}+\mathrm{n}_{2}\right)\right\\}\)

Short Answer

Expert verified
The time interval to obtain a beat of maximum intensity is (A) \(\left\\{1 /\left(\mathrm{n}_{1}-\mathrm{n}_{2}\right)\right\\}\).

Step by step solution

01

Identify Given Values

We are given almost identical waves having frequencies n1 and n2. We need to find the time interval to obtain a beat of maximum intensity.
02

Calculate The Beat Frequency

The beat frequency is the difference in frequencies of the two waves (n1 and n2). Beat Frequency (BF) = \(|n_1 - n_2|\)
03

Calculate The Time Interval for Maximum Intensity Beat

The time interval for a beat of maximum intensity is the inverse of the beat frequency. Time interval (T) = \(\frac{1}{BF}\) = \(\frac{1}{|n_1 - n_2|}\)
04

Check The Answer with The Given Options

Comparing the result, we have Time Interval (T) = \(\frac{1}{|n_1 - n_2|}\). The correct answer is (A) \(\left\\{1 /\left(\mathrm{n}_{1}-\mathrm{n}_{2}\right)\right\\}\).

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