Exams › JEE Advanced › Physics

A closed organ pipe of length 28 cm (closed at one end) resonates with a tuning fork of frequency 850 Hz. The speed of sound in air is 340 m/s. Which of the following statements are correct? (A) The end correction of the pipe is 1 cm (B) The end correction of the pipe is 2 cm (C) The air column vibrates in its fundamental mode (D) The air column vibrates in the first overtone

1. The end correction of the pipe is 1 cm
2. The end correction of the pipe is 2 cm
3. The air column vibrates in its fundamental mode
4. The air column vibrates in the first overtone

Correct answer: The end correction of the pipe is 1 cm

Solution

For a closed pipe resonating at frequency f, the effective length is L_eff = (2n-1)*v/(4f). With v=340 m/s, f=850 Hz: L_eff = (2n-1)*340/(4*850) = (2n-1)*0.1 m. For n=1: L_eff=0.10 m; n=2: L_eff=0.30 m; n=3: L_eff=0.50 m. Since L=0.28 m, n=2 gives L_eff=0.30 m, so end correction e = 0.30-0.28 = 0.02 m = 2 cm. n=2 means first overtone (3rd harmonic).

Related JEE Advanced Physics questions

• A wave pulse traveling to the right along the x-axis is described by the equation y(x, t) = 2.0 / ((x − 3.0t)² + 1), where x and y are measured in centimeters and t is in seconds. The peak height of the pulse is defined as the largest displacement along the y-axis. Which of the following is true?
• When a person blows into one end of a long pipe, creating a high-pressure air pulse that moves through it, what happens when this pulse reaches the opposite end of the pipe?
• Under which condition can stationary waves form?
• Four harmonic waves of equal frequencies and equal intensities I₀ have phase angles 0, π/3, 2π/3, and π. When they are superposed, the intensity of the resulting wave is nI₀. The value of n is
• A string that is 1 meter long and has a mass of 2 × 10⁻⁵ kg is stretched under a tension T. When vibrating, it produces two consecutive harmonics with frequencies of 750 Hz and 1000 Hz. What is the value of the tension T in Newtons?
• A plane progressive wave travels in the +x direction and is described by y = 0.02 sin(8*pi*(t - x/20)). It is reflected at a rarer medium (a medium in which wave speed is higher) at x = 0. The amplitude of the reflected wave is 75% of the incident amplitude. What is the equation of the reflected wave?

⚔️ Practice JEE Advanced Physics free + battle 1v1 →