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JEE Main & Advanced Physics Wave Mechanics Question Bank Self Evaluation Test - Waves

  • question_answer
    A plane progressive simple harmonic sound wave of angular frequency \[680\text{ }rad/s\] moves with speed 340 m/s in the direction which makes equal angle with each x, y and z-axis. The phase difference (\[{{\phi }_{1}}-{{\phi }_{2}}\]) between the oscillations of the particle in the medium located at the positions \[(\sqrt{3,}\sqrt{3,}\sqrt{3})\]and \[(2\sqrt{3,}\,2\sqrt{3,}\,2\sqrt{3})\] is (assume\[\cos \theta >0\])

    A)  2 radian

    B)  3 radian

    C) 4 radian

    D) 6 radian

    Correct Answer: D

    Solution :

    [d] \[y(\overset{\to }{\mathop{r}}\,,t)=A\,\sin (\omega t-\overset{\to }{\mathop{k}}\,.\overset{\to }{\mathop{r}}\,)\] \[\hat{k}=\frac{2\pi }{\lambda }(\cos \alpha \hat{i}+\cos \beta \hat{j}+\cos \gamma \hat{k})=\frac{k}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})\] \[{{\phi }_{1}}-{{\phi }_{2}}=2(3)=6\,rad.\]


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