Sound WavesHardBloom L3
Question
A plane transverse wave is propagating in a direction making an angle of 30° with positive x-axis in the x-y plane. Find phase difference between points (0, 0, 0) and (1, 1, 1). Wavelength of the wave is 1m
Options
A.2π rad
B.$(\sqrt{3} + 1)\pi$rad
C.$(\sqrt{2} + 1)\pi$rad
D.None
Solution
Sol. 
$\overrightarrow{B} = \frac{\sqrt{3}}{2}\widehat{i} + \frac{1}{2}\widehat{j}$
$\overrightarrow{A} = \widehat{i} + \widehat{j} + \widehat{k}$
∆φ = $\frac{2\pi}{\lambda}$ : ∆x
∆x = $\overrightarrow{A} \cdot \overrightarrow{B} = \frac{\sqrt{3}}{2} + \frac{1}{2} = \frac{\sqrt{3} + 1}{2}$ ⇒ $\frac{2\pi}{1} \times \frac{\left( \sqrt{3} + 1 \right)}{2}$
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