Question:
For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m, while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in m) of the waves are :
For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m, while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in m) of the waves are :
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The distance between two crests is \(n\lambda\); the distance between a crest and a trough is \((m + \tfrac{1}{2})\lambda\). Both conditions must hold together.
Updated On: Nov 5, 2026
- \(1, 2, 3, \ldots\)
- \(1, 3, 5, \ldots\)
- \(\frac{1}{1}, \frac{1}{3}, \frac{1}{5}, \ldots\)
- \(\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \ldots\)
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The Correct Option is C
Solution and Explanation
Two crests are separated by a whole number of wavelengths: \(n\lambda = 5\), so \(\lambda = 5/n\) with \(n = 1, 2, 3, \ldots\).
A crest and a trough are separated by an odd number of half wavelengths: \((2m+1)\dfrac{\lambda}{2} = 1.5\), so \(\lambda = \dfrac{3}{2m+1}\) with \(m = 0, 1, 2, \ldots\).
Hence \(5/\lambda\) must be an integer and \(3/\lambda\) must be an odd integer.
Try \(\lambda = 1/k\): \(5/\lambda = 5k\) (always an integer) and \(3/\lambda = 3k\), which is odd only for odd \(k\). So \(\lambda = \frac{1}{1}, \frac{1}{3}, \frac{1}{5}, \ldots\) m.
Check against the others: \(\lambda = 2\) gives \(5/2\), not an integer; \(\lambda = 3\) gives \(5/3\), not an integer; \(\lambda = \frac12\) gives \(3/\lambda = 6\), which is even.
Answer: (3) \(\frac{1}{1}, \frac{1}{3}, \frac{1}{5}, \ldots\)
A crest and a trough are separated by an odd number of half wavelengths: \((2m+1)\dfrac{\lambda}{2} = 1.5\), so \(\lambda = \dfrac{3}{2m+1}\) with \(m = 0, 1, 2, \ldots\).
Hence \(5/\lambda\) must be an integer and \(3/\lambda\) must be an odd integer.
Try \(\lambda = 1/k\): \(5/\lambda = 5k\) (always an integer) and \(3/\lambda = 3k\), which is odd only for odd \(k\). So \(\lambda = \frac{1}{1}, \frac{1}{3}, \frac{1}{5}, \ldots\) m.
Check against the others: \(\lambda = 2\) gives \(5/2\), not an integer; \(\lambda = 3\) gives \(5/3\), not an integer; \(\lambda = \frac12\) gives \(3/\lambda = 6\), which is even.
Answer: (3) \(\frac{1}{1}, \frac{1}{3}, \frac{1}{5}, \ldots\)
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