Question

The rope shown at an instant is carrying a wave travelling towards right, created by a source vibrating at a frequency $n$. Choose the correct statement(s).

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• A. The speed of the wave is $4n\times ab$
• B. The medium at a will be in the same phase as d after $\frac{4}{3n}\text{s}$
• C. The phase difference between b and e is $\frac{3\pi }{2}$
• D. The speed of the wave is $2n\times ab$

Answer 1

Answer: (A), (C)

The correct options are
A The speed of the wave is $4n\times ab$
C The phase difference between b and e is $\frac{3\pi }{2}$

From the figure
$ab=\frac{\lambda }{4}$
Speed $=n\lambda$
$=(n\times 4ab)$
Path difference between b and e is $\left(\frac{3\lambda }{4}\right)$
$\therefore$ Phase difference = $\frac{2\pi }{\lambda }\times$ Path difference
$=\frac{2\pi }{\lambda }\times \frac{3\lambda }{4}$
$=\frac{3\pi }{2}$
Path difference between a and d $=\frac{3\lambda }{4}$
Also, time difference between a and d $=\frac{T}{\lambda }\times \frac{3\lambda }{4}=\frac{3T}{4}=\frac{3}{4n}$
[$\because T=\frac{1}{n}$]
Hence A, C are correct.