question_answer

Three sound waves of equal amplitudes have frequencies\[(v1),v,(v+1).\]They superpose to give beats. The number of beats produced per second will be     AIEEE  Solved  Paper-2009

A) 4

B)                                       3                             

C)        2                             

D)        1.

Correct Answer: C

Solution :

\[{{p}_{1}}={{p}_{o}}\sin 2\pi (x-1)t\] \[{{p}_{2}}={{p}_{o}}\sin 2\pi (x)t\] \[{{p}_{3}}={{p}_{o}}\sin 2\pi (x+1)t\] \[p={{p}_{1}}+{{p}_{3}}+{{p}_{2}}\] \[={{p}_{o}}\sin 2\pi (x-1)t+{{p}_{o}}\sin 2\pi (x+1)t+{{p}_{o}}\sin 2\pi ct\] \[=2{{p}_{o}}sin2\pi xt\text{ }cos2\pi t+{{p}_{o}}sin2\pi xt\] \[={{p}_{o}}sin2\pi xt[2cos\pi t+1]\] \[\Rightarrow \] \[{{f}_{beat}}=2.\]