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Stage 2 – Page 7 : Resonance Tube Experiment & Velocity of Sound
1️⃣ What Is Resonance?
Resonance occurs when the frequency of the sound source matches the natural frequency of the air column.
At resonance → amplitude becomes maximum → sound becomes loud.
2️⃣ Resonance Tube Experiment Setup
- Vertical glass tube partially filled with water
- Tuning fork of known frequency
- Air column above water acts as a closed pipe
3️⃣ Resonance Condition for Closed Pipe
Leff = (2n − 1) λ / 4
Only odd harmonics are possible.
4️⃣ First Resonance (Fundamental)
L₁ + e = λ / 4
This gives the smallest air column length.
5️⃣ Second Resonance
L₂ + e = 3λ / 4
Difference between two resonance lengths eliminates end correction.
6️⃣ Key Relation (Most Important)
L₂ − L₁ = λ / 2
This relation is heavily used in JEE numericals.
7️⃣ Velocity of Sound Formula
v = fλ
Using resonance:
v = 2f (L₂ − L₁)
8️⃣ Why Use Difference of Lengths?
- End correction cancels out
- Gives more accurate velocity
- Used in experiments & exams
9️⃣ JEE-Type Conceptual Traps
- Resonance tube is always a closed pipe
- Do not apply open pipe formula
- Use L₂ − L₁, not absolute length
🔟 Typical JEE Question
Given f = 512 Hz, L₁ = 16 cm, L₂ = 49 cm. Find velocity of sound.
Method: v = 2f (L₂ − L₁)
➡️ Next Page Preview
- Beats & beat frequency
- Applications in sound tuning
Stage 2 – Page 7 Completed Successfully ✅
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