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Physics-

General

Easy

Question

Two sound waves are superimposed. The resulting pressure variation at a single point at a distance 'x' from the source is graphed below :

The beat frequency of the resulting sound wave is :

10 Hz
20 Hz
5 Hz
40 Hz

The correct answer is: 10 Hz

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If roots of the eduation $open parentheses blank to the power of m end exponent C subscript 0 end subscript plus blank to the power of m end exponent C subscript 1 end subscript midline horizontal ellipsis blank to the power of m end exponent C subscript m end subscript close parentheses x to the power of 2 end exponent plus open parentheses blank to the power of n end exponent C subscript 0 end subscript plus blank to the power of n end exponent C subscript 2 end subscript plus blank to the power of n end exponent C subscript 4 end subscript midline horizontal ellipsis close parentheses x plus open parentheses blank to the power of n end exponent C subscript 1 end subscript plus blank to the power of n end exponent C subscript 3 end subscript plus blank to the power of n end exponent C subscript 5 end subscript midline horizontal ellipsis close parentheses equals 0$ are real, then find the minimum value of n –m.

If roots of the eduation $open parentheses blank to the power of m end exponent C subscript 0 end subscript plus blank to the power of m end exponent C subscript 1 end subscript midline horizontal ellipsis blank to the power of m end exponent C subscript m end subscript close parentheses x to the power of 2 end exponent plus open parentheses blank to the power of n end exponent C subscript 0 end subscript plus blank to the power of n end exponent C subscript 2 end subscript plus blank to the power of n end exponent C subscript 4 end subscript midline horizontal ellipsis close parentheses x plus open parentheses blank to the power of n end exponent C subscript 1 end subscript plus blank to the power of n end exponent C subscript 3 end subscript plus blank to the power of n end exponent C subscript 5 end subscript midline horizontal ellipsis close parentheses equals 0$ are real, then find the minimum value of n –m.

For $x blank R blank element of comma blank x blank not equal to blank minus 1 comma$ if $left parenthesis 1 plus x right parenthesis to the power of 2016 end exponent plus x left parenthesis 1 plus x right parenthesis to the power of 2015 end exponent plus x to the power of 2 end exponent left parenthesis 1 plus x right parenthesis to the power of 2014 end exponent plus midline horizontal ellipsis plus x to the power of 2016 end exponent equals stretchy sum from i equals 0 to 2016 of a subscript i end subscript x to the power of i end exponent$ then $a subscript 17 end subscript blank$ is equal to

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The term independent of x in expansion of $blank open parentheses fraction numerator x plus 1 over denominator x to the power of 2 divided by 3 end exponent minus x to the power of 1 divided by 3 end exponent plus 1 end fraction minus fraction numerator x minus 1 over denominator x minus x to the power of 1 divided by 2 end exponent end fraction close parentheses to the power of 10 end exponent$ is

The term independent of x in expansion of $blank open parentheses fraction numerator x plus 1 over denominator x to the power of 2 divided by 3 end exponent minus x to the power of 1 divided by 3 end exponent plus 1 end fraction minus fraction numerator x minus 1 over denominator x minus x to the power of 1 divided by 2 end exponent end fraction close parentheses to the power of 10 end exponent$ is

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