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NEET PHYSICSWAVEMedium

Question

Two sources of sound placed close to each other, are emitting progressive waves given by y1=4sin(600πt)y_1 = 4 \sin(600\pi t) and y2=5sin(608πt)y_2 = 5 \sin(608\pi t). An observer located near these two sources of sound will hear

A

44 beats per second with intensity ratio 25:1625:16 between waxing and waning

B

88 beats per second with intensity ratio 25:1625:16 between waxing and waning

C

88 beats per second with intensity ratio 81:181:1 between waxing and waning

D

44 beats per second with intensity ratio 81:181:1 between waxing and waning

Step-by-Step Solution

  1. Determine Frequencies: Compare the given wave equations y1=4sin(600πt)y_1 = 4 \sin(600\pi t) and y2=5sin(608πt)y_2 = 5 \sin(608\pi t) with the standard wave equation y=Asin(ωt)y = A \sin(\omega t), where ω=2πf\omega = 2\pi f. For the first wave: ω1=600π    2πf1=600π    f1=300 Hz\omega_1 = 600\pi \implies 2\pi f_1 = 600\pi \implies f_1 = 300 \text{ Hz} For the second wave: ω2=608π    2πf2=608π    f2=304 Hz\omega_2 = 608\pi \implies 2\pi f_2 = 608\pi \implies f_2 = 304 \text{ Hz}
  2. Calculate Beat Frequency: The beat frequency is the difference between the two frequencies : fbeat=f1f2=300304=4 beats/sf_{\text{beat}} = |f_1 - f_2| = |300 - 304| = 4 \text{ beats/s}
  3. Determine Amplitudes and Intensity Ratio: The amplitudes of the waves are A1=4A_1 = 4 and A2=5A_2 = 5. The intensity of a wave is directly proportional to the square of its amplitude (IA2I \propto A^2).
  • For waxing (constructive interference/maximum intensity): Imax(A1+A2)2=(4+5)2=92=81I_{\max} \propto (A_1 + A_2)^2 = (4 + 5)^2 = 9^2 = 81 .
  • For waning (destructive interference/minimum intensity): Imin(A1A2)2=(45)2=(1)2=1I_{\min} \propto (A_1 - A_2)^2 = (4 - 5)^2 = (-1)^2 = 1 .
  • The intensity ratio between waxing and waning is therefore Imax:Imin=81:1I_{\max} : I_{\min} = 81:1.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from WAVE. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSWAVEsourcesplacedemittingprogressiveobserver

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