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🌊 WAVES (Mechanical Waves)

Stage 2 – Page 6 : End Correction & Effective Length of Air Columns

1️⃣ Why End Correction Is Needed?

In real pipes, sound waves do not reflect exactly at the open end. The air just outside the pipe also vibrates.

Result: Effective length of the air column becomes slightly longer than the actual length.

2️⃣ What Is End Correction?

End correction (e) is the additional length added to the pipe length due to vibration of air outside the open end.

e ≈ 0.6r

where r = radius of the pipe.

3️⃣ End Correction Rules

Only open ends need end correction
Closed ends → No end correction
Depends on radius, not length

4️⃣ Effective Length of Open Pipe

Open pipe has two open ends.

L_eff = L + 2e

L_eff = L + 1.2r

5️⃣ Effective Length of Closed Pipe

Closed pipe has only one open end.

L_eff = L + e

L_eff = L + 0.6r

6️⃣ Modified Frequency Formula (Open Pipe)

fₙ = n × v / (2L_eff)

Always use effective length in calculations.

7️⃣ Modified Frequency Formula (Closed Pipe)

fₙ = (2n − 1) × v / (4L_eff)

End correction increases wavelength → frequency decreases.

8️⃣ JEE Conceptual Points

Ignoring end correction gives higher frequency
Used in tuning forks + resonance tube experiments
More significant for short pipes

9️⃣ Typical JEE Question Idea

A pipe of length L resonates at frequency f. Find new frequency when radius is doubled.

Hint: End correction changes → effective length changes → frequency changes.

🔟 Next Page Preview

Resonance tube experiment
Finding velocity of sound

Stage 2 – Page 6 Completed Successfully ✅