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Question: When two waves of almost equal frequencies \(\upsilon_{1}\) and \(\upsilon_{2}\) reach at a point si...

When two waves of almost equal frequencies υ1\upsilon_{1} and υ2\upsilon_{2} reach at a point simultaneously, the time interval between successive maxima is

A

υ1+υ2\upsilon_{1} + \upsilon_{2}

B

υ1−υ2\upsilon_{1} - \upsilon_{2}

C

1υ1+υ2\frac{1}{\upsilon_{1} + \upsilon_{2}}

D

1υ1−υ2\frac{1}{\upsilon_{1} - \upsilon_{2}}

Answer

1υ1−υ2\frac{1}{\upsilon_{1} - \upsilon_{2}}

Explanation

Solution

When two waves of almost equal frequencies υ1\upsilon_{1}and υ2\upsilon_{2}reach at a point simultaneously, beats are produced. Beat frequency,

υbest=υ1−υ2\upsilon_{best} = \upsilon_{1} - \upsilon_{2}

Time interval between successive maxima

1υbeat=1υ1−υ2\frac{1}{\upsilon_{beat}} = \frac{1}{\upsilon_{1} - \upsilon_{2}}