The Question is from neet-physics waves velocity-of-sound, and it was created by the author P.NARASIMHA

Question

Two sound waves of equal amplitude and slightly different frequencies $f_1$ and $f_2$ are travelling in the same direction. The time interval between successive maxima of intensity is:

P.NARASIMHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
 **Primary Concept**: Interference of waves, beats
 **Related Topics**: Superposition principle, wave propagation
 **Prerequisites**: Understanding of wave interference, frequency, and beat frequency.
## SOLUTION PATHWAY
**Given Information**:
  Two sound waves with frequencies $f_1$ and $f_2$ and equal amplitudes are travelling in the same direction.
  The waves interfere, creating a beat pattern.
**Method & Steps**:
 1. Understanding Beat Frequency:
  Reasoning: When two waves of slightly different frequencies interfere, the resultant wave's amplitude varies periodically. This variation in amplitude creates beats. The beat frequency ($f_b$) is the difference between the two frequencies.
  Formula/Rule: $f_b = |f_1 - f_2|$ 
 2. Relating Beat Frequency to Time Interval:
  Working: The time interval between successive maxima of intensity (beat period) is the reciprocal of the beat frequency.
  Formula/Rule: $T_b = \frac{1}{f_b}$
 3. Calculating Time Interval:
  Result: Substituting the beat frequency, we get the time interval between successive maxima of intensity as $T_b = \frac{1}{|f_1 - f_2|}$ 
  Verification: The units are consistent (1/frequency = time).
 ## OPTION ANALYSIS
A :x: This option gives the reciprocal of the sum of frequencies, which is incorrect. The time interval is related to the difference in frequencies.
B :x: This option is almost correct, but it misses the absolute value. The beat frequency is always positive.
C ✓: This option correctly represents the time interval between successive maxima of intensity as the reciprocal of the absolute difference between the two frequencies.
D :x: This option is incorrect. It involves the sum of frequencies, not the difference.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing beat frequency with the average frequency: The beat frequency is the difference, not the average, of the two frequencies.
  2.Forgetting the absolute value: The beat frequency is always positive, so the absolute difference must be considered.
 **Quick Tips**:
  1.Remember that the beat frequency is the difference between the two frequencies, and the time period is the reciprocal of the frequency.
  2.Visualize the interference pattern to understand how the amplitude varies periodically.

P.NARASIMHA · Answer

$\frac{1}{f_1 + f_2}$

P.NARASIMHA · Answer

$\frac{1}{f_1 - f_2}$

P.NARASIMHA · Answer

The correct Option is "$\frac{1}{|f_1 - f_2|}$"

P.NARASIMHA · Answer

$\frac{2}{f_1 + f_2}$

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