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Chapter 10: Problem 1429

The ratio of frequencies of two waves travelling through the same medium is \(2: 5 .\) The ratio of their wavelengths will be.... (A) \(2: 5\) (B) \(5: 2\) (C) \(3: 5\) (D) \(5: 3\)

Short Answer

Expert verified
The ratio of the wavelengths of the two waves is 5:2. Hence, the correct answer is (B) \(5: 2\).

Step by step solution

01

Understand the relationship between frequency and wavelength.

The fundamental relationship between the frequency (f), wavelength (λ), and wave speed (v) is given by the following equation: \(v = fλ\) Since both waves are traveling through the same medium, their wave speeds will be the same.
02

Write two equations for the two waves.

Let: Wave 1: frequency = f1, wavelength = λ1 Wave 2: frequency = f2, wavelength = λ2 Using the fundamental relationship, we have two equations \(v = f_1λ_1\) \(v = f_2λ_2\) Given, the ratio of frequencies of two waves is 2:5. \(f_1/f_2 = 2/5\) or \(f_2 = \frac{5}{2}f_1\)
03

Substitute the ratio of frequencies and solve for the ratio of wavelengths.

Now, we'll substitute the value of f2 into the second equation in terms of f1 and then divide the first equation by the second equation. \(\frac{v}{f_1λ_1} = \frac{v}{\frac{5}{2}f_1λ_2} \)
04

Simplify the equation and find the ratio of the wavelengths (λ1: λ2).

Now, simplify the equation by canceling out common terms and obtain the ratio of \(\lambda_1 : \lambda_2 \): \(\frac{\lambda_1}{\lambda_2} = \frac{5}{2} \) Thus, the ratio of the wavelengths of the two waves is 5:2. The correct answer is (B) \(5: 2\).

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Most popular questions from this chapter

The maximum velocity and maximum acceleration of a particle executing S.H.M. are \(1 \mathrm{~m} / \mathrm{s}\) and \(3.14 \mathrm{~m} / \mathrm{s}^{2}\) respectively. The frequency of oscillation for this particle is...... (A) \(0.5 \mathrm{~s}^{-1}\) (B) \(3.14 \mathrm{~s}^{-1}\) (C) \(0.25 \mathrm{~s}^{-1}\) (D) \(2 \mathrm{~s}^{-1}\)

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