Exams › JEE Advanced › Physics

A closed organ pipe and an open organ pipe are tuned so that their first overtones have the same frequency. What is the ratio of the length of the closed pipe to the length of the open pipe?

1. 1: 2
2. 2: 3
3. 3: 4
4. 4: 5

Correct answer: 3: 4

Solution

For a closed pipe the harmonics present are odd multiples of v/(4L_c). The first overtone is the 3rd harmonic: f_c = 3v/(4L_c). For an open pipe the harmonics present are all multiples of v/(2Lₒ). The first overtone is the 2nd harmonic: fₒ = 2v/(2Lₒ) = v/Lₒ. Setting equal: 3v/(4L_c) = v/Lₒ gives L_c/Lₒ = 3/4.

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 →