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NEET Physics Wave Mechanics NEET PYQ-Wave Mechanics

  • question_answer
    A point source emits sound equally in all directions in a non-absorbing medium. Two points P and Q are at distance of 2 m and 3 m respectively from the source. The ratio of the intensities of the waves at P and Q is:                      [AIPMT (S) 2005]

    A)  9 : 4      

    B)                  2 : 3                

    C)  3 : 2     

    D)                   4 : 9

    Correct Answer: A

    Solution :

    Key Idea: The average power per unit area that is incident perpendicular to the direction of propagation is called the intensity.
                Intensity of sound
                            \[I=\frac{P}{4\pi {{r}^{2}}}\]
                or         \[I\,\propto \,\frac{1}{{{r}^{2}}}\]
                or         \[\frac{{{I}_{1}}}{{{I}_{2}}}={{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}\]
                Here,     \[{{r}_{1}}=2\,m,\,{{r}_{2}}=3\,m\]
                Substituting the values, we have
                            \[\frac{{{I}_{1}}}{{{I}_{2}}}={{\left( \frac{3}{2} \right)}^{2}}=\frac{9}{4}\]
    Note:    As amplitude \[A\propto \sqrt{l},\] a spherical harmonic wave emanating from a point source can therefore, be written as:
    \[y(r,\,t)=\frac{A}{r}\sin (kr-\omega t)\]


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