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Physics · Class 11

Combine nearby frequencies

Waves

Nearby tones alternate between constructive and destructive interference. The loudness envelope repeats at the difference frequency. The signed envelope has twice the intensity-peak spacing because positive and negative peaks both correspond to loud sound.

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Combine nearby frequencies

அருகிலுள்ள இரு அதிர்வெண்கள் சேரும்போது ஒலி வீச்சு மாறி துடிப்பு உருவாகும். துடிப்பு அதிர்வெண் |f₁−f₂|.

Key notes, relationships and model limits

Key relationship

sin(2πf₁t)+sin(2πf₂t)=2cos(π(f₁−f₂)t)sin(π(f₁+f₂)t); fbeat=|f₁−f₂|.

Remember

Nearby tones alternate between constructive and destructive interference. The loudness envelope repeats at the difference frequency. The signed envelope has twice the intensity-peak spacing because positive and negative peaks both correspond to loud sound.

Common trap

The beat frequency is the difference, not the average, of the two tones.

Model limits

Equal-amplitude coherent nearby tones; envelope is plotted separately from the fast acoustic carrier. At larger differences the modulation becomes rapid. Use the optional sound control to hear both tones.

What you will learn

Connect tone frequency difference to periodic amplitude modulation.

Try the experiment

Try both scenarios, change one control, and predict the result before checking the graph and readouts.

Think of it this way

Change one input while keeping the others fixed, as you would in a controlled experiment.

Worked example

The carrier is near 202 Hz; loudness maxima occur every 0.25 s. At t=0.125 s the equal tones cancel in their envelope.

Why this matters

The model connects combine nearby frequencies with an observable reading. Check the equation and assumptions before applying it.

Before you start

SI units · algebra · graph reading

Check your understanding

What beat frequency comes from 200 Hz and 204 Hz?

Read the explanation

The absolute frequency difference is |200−204|=4 Hz.

Course connection: Class XI Chapter 14. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.