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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2006

  • question_answer
        The number of beats produced per second by two vibrations\[{{x}_{1}}={{x}_{0}}\]and\[{{x}_{2}}={{x}_{0}}\sin 652\pi t\]is

    A)  2                                            

    B)  3

    C)  4                                            

    D)  6

    Correct Answer: B

    Solution :

                    Beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies. The standard wave equation is \[x={{x}_{0}}sin\text{ }2\pi nt.\] Given, equations are                 \[{{x}_{1}}={{x}_{0}}sin\text{ 646}\pi t\]                 \[{{x}_{2}}={{x}_{0}}sin\text{ 652}\pi t\] Comparing with standard equation we get \[2{{n}_{1}}=646\Rightarrow {{n}_{1}}=323\] \[2{{n}_{2}}=652\Rightarrow {{n}_{2}}=326\] So, number of beats per second \[=326-323=3.\]


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