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Waves question

2012 · Q170
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Waves question

2012 · Q170

NEETPhysicsWavesMCQ+4 / −1
Two sources of sound placed close to each other, are emitting progressive waves given by
y1 = 4sin600π\piπt and y2 = 5sin608π\piπt
An observer located near these two sources of sound will hear
  1. A
    4 beats per second with intensity ratio 25 : 16 between waxing and waning.
  2. B
    8 beats per second with intensity ratio 25 : 16 between waxing and waning.
  3. C
    8 beats per second with intensity ratio 81 : 1 between waxing and warning.
  4. D
    4 beats per second with intensity ratio 81 : 1 between waxing and waning.
View written solutionFree

Correct answer: D

2πf1=600π2\pi {f_1} = 600\pi 2πf1​=600π

f1=300{f_1} = 300f1​=300   ...(i)

2πf2=608π2\pi {f_2} = 608\pi 2πf2​=608π

f2=304{f_2} = 304f2​=304   ...(ii)

∣f1−f2∣=4 beats\left| {{f_1} - {f_2}} \right| = 4\,beats∣f1​−f2​∣=4beats

Imax⁡Im.n=(A1+A2)2(A1+A2)2=(5+4)2(5−4)2=811{{{I_{\max }}} \over {{I_{m.n}}}} = {{{{\left( {{A_1} + {A_2}} \right)}^2}} \over {{{\left( {{A_1} + {A_2}} \right)}^2}}} = {{{{\left( {5 + 4} \right)}^2}} \over {{{\left( {5 - 4} \right)}^2}}} = {{81} \over 1}Im.n​Imax​​=(A1​+A2​)2(A1​+A2​)2​=(5−4)2(5+4)2​=181​

where A1, A2 are amplitudes of given two sound wave.

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