NTA Abhyas JEE Main2020PhysicsWaves and SoundPractice
The air column in a pipe closed at one end is made to vibrate in its second overtone by a tuning fork of frequency 440 Hz . The speed of the sound in air is 330 m s - 1 . End corrections may be neglected. Let P 0 denote the mean pressure at any point in the pipe and ∆ P 0 the maximum amplitude of pressure variation then the amplitude of pressure variation in the middle of the column is
Options
- A∆ p 2 2
- B∆ p 0 3
- C∆ p 0 2
- D∆ p 0 3
Correct answer
A. ∆ p 2 2
Step-by-step solution
P = ∆ P 0 sin ⁡ 2 π x λ For the second overtone L = 5 λ 4 At   x = L 2 = 5 λ 8 Pressure amplitude at middle p = ∆ P 0 sin ⁡ 2 π λ 5 λ 8 ∆ P 0 sin ⁡ 5 π 4 = ∆ P 0 2