An organ pipe P1, closed at one end vibrating in its first harmonic, and another pipe P2 open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 is:
Correct answer: C. 1/6
- A. 8/3
- B. 3/8
- C. 1/6
- D. 1/3
Explanation
An organ pipe closed at one end (P1) vibrating in its first harmonic has a wavelength of 4 times the length of the pipe (since it forms a quarter-wavelength standing wave). An open pipe (P2) vibrating in its third harmonic has a wavelength equal to twice the length of the pipe divided by 3 (since it forms a three-quarter wavelength standing wave). For both pipes to be in resonance with the same tuning fork, their frequencies must be equal. Thus, the ratio of the lengths of P1 to P2 is determined by the ratio of their respective wavelengths, leading to a calculated ratio of 1/6. This results from equating the frequency expressions of the two pipes and solving for the length ratio. The other options do not correctly apply these relationships.v=v/4l1 for first harmonic v=3v/2l2 for third harmonic v/4l1=3v/2l2 l1/l2=1/6
Report an error
The more specific you are, the faster it gets fixed. A source beats an opinion.
Prefer email? [email protected]
About Waves
Progressive waves transfer energy through oscillations, with wavelength, frequency, amplitude and wave speed related by v = fλ; sound speed depends on the medium. Superposition produces interference and stationary waves in strings and organ pipes, while simple harmonic motion describes the oscillation itself and must be distinguished from wave propagation.
Practise Waves
1,281 free Waves MCQs from Physics, each with the correct answer and an explanation. Unlimited attempts, no account needed.
Discussion
Stuck on an option, or know a faster way to get there? Ask or explain it here.
No comments yet. Be the first to explain this one.
Exams that ask Physics questions like this
Physics is on 16 papers prepared for on TestUstad, and all of them draw the same bank, so this question is worth knowing for every one of them.
More Waves questions
When the source is at the centre of the circle and the observer is moving on the circumference of circle, the sound heard by observer:
A tuning fork A produces 4 beats / second with another turning fork B of frequency 280 Hz. When fork A is loaded with a little wax, the beat frequency change to 2. The frequency of fork A before loading is:
When path difference between two waves are integral multiple of wavelength, the resultant effect is called _.
For a closed organ pipe, three successive resonance frequencies are observed at 425 Hz, 595 Hz, and 765 Hz respectively. If the speed of sound in air is 340 m/s, then the length of the pipe is:
The displacement of particles in a string stretched in the x-direction is represented by y. Among the following expressions for y, those describing wave motion are:
An open pipe is suddenly closed at one end with the result that the frequency of the third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is: