Advertisements
Advertisements
Question
Find the fundamental, first overtone, and second overtone frequencies of a pipe, open at both the ends, of length 25 cm if the speed of sound in air is 330 m/s.
Advertisements
Solution
Data: Open pipe, L = 25 cm = 0.25 m, v = 330 m/s The fundamental frequency of an open pipe ignoring end correction,
nO = `"v"/λ="v"/(2"L")`
∴ nO = `330/(2xx0.25)` = 660 Hz
Since all harmonics are present as overtones, the first overtone is,
n1 = 2nO = 2 × 660 = 1320 Hz
The second overtone is
n2 = 3n = 3 × 660 = 1980 Hz
APPEARS IN
RELATED QUESTIONS
Answer in brief:
What are harmonics and overtones?
A pipe open at both the ends has a fundamental frequency of 600 Hz. The first overtone of a pipe closed at one end has the same frequency as the first overtone of the open pipe. How long are the two pipes?
(Given: v = 330 m/s)
The equation of a simple harmonic progressive wave is given by, y = 5cosπ`[200t - x/150]`, where x and y are in cm and ‘t’ is in second. Then the velocity of the wave is ______.
A violin string vibrates with the fundamental frequency of 510 Hz. What is the frequency of the first overtone?
An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of open pipe to that of closed pipe is ______.
Two identical strings of length I and 2I vibrate with fundamental frequencies N Hz and 1.5 N Hz, respectively. The ratio of tensions for smaller length to large length is ____________.
At the poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting to produce resonance with same fork. the vibrating length of wire ______.
Two open pipes of different lengths and same diameter in which the air column vibrates with fundamental frequencies 'n1', and 'n2' respectively. When both pipes are joined to form a single pipe, its fundamental frequency will be ______.
A tube closed at one end and containing air produces fundamental note of frequency 256 Hz. If the tube is open at both ends, the fundamental frequency will be ____________.
An open organ pipe produces its fundamental frequency f. When the pipe is dipped in water so that `2/5` of its length is under water, then its 5 fundamental frequency becomes ____________.
If we study the vibration of a pipe open at both ends, then which of the following statements is not true?
'n' number of waves are produced on a string in 0.5 seconds. Now the tension in a string is doubled (Keeping radius constant). The number of waves produced in 0.5 seconds for the same harmonic will be ______
The sequence of harmonics of a pipe open at one end and closed at the other end is 250 Hz and 350 Hz, The resonating length of the air column in its fundamental mode will be ______
(velocity of sound in air = 340 m/s)
The equation of simple harmonic wave is given as y = 5sin `pi/2(100t - x)`, where 'x' and 'y' are in metre and time in second. The period of the wave is ______
A pipe closed at one end produces a fundamental note of frequency 'v'. It is cut into two pipes of equal length. The fundamental frequencies produced in the two pipes are ______.
The equation of stationary wave on a string clamped at both ends and vibrating in the third harmonic is given by y = 0.5 sin (0.314 x) cos (600 πt), where x and y are in cm and t in second. The length of the vibrating string is ______
(π = 3.14)
An organ pipe P1 closed at one end vibrating in its first overtone and another pipe P2 open at both ends vibrating in third overtone are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 is ______.
The fundamental frequency of an air column is a pipe closed at one end is 100 Hz. If the same pipe is open at both the ends, the frequencies produced in Hz are ______.
A pipe Pc closed at one end and point Po open at both ends are vibrating in the second overtone. They are in resonance with a given tuning fork. The ratio of the length of pipe Pc to that of pipe, Po is ______.
(Neglect end correction).
An open pipe is in resonance in its 2nd harmonic with tuning fork of frequency f1. Now, it is closed at one end. If the frequency of the tuning fork is increased slowly from f1, then again a resonance is obtained with a frequency f2. If in this case the pipe vibrates nth harmonic, then ______.
Two organ pipes closed at one end have the same diameters but different lengths. Show that the end correction at each end is e = `(n_1l_1 - n_2l_2)/(n_2 - n_1)`, where the symbols have their usual meanings. Take `γ = 5/3`.
Two consecutive harmonics of air column in a pipe closed at one end are frequencies 150 Hz and 250 Hz. Calculate the fundamental frequency.
Two organ pipe, open at both ends, are sounded together and 5 beats are heard per second. The length of shorter pipe is 0.25 m. Find the length of the other pipe. (Given: Velocity of sound in air = 350 m/s and end correction at one end = 0.015 m, same for both pipes.)
A wire of length L, diameter 'd' density of material 'e' is under tension 'T', having fundamental frequency of vibration nA. Another wire of length 2L, tension 2T, density 2e and diameter 3d has fundamental frequency of vibration nB. The ratio nB: NA is ______.
A string of mass ‘M’ is under a tension ‘T’. The length of the string is ‘L’. A transverse wave starts from one end of the string. The time taken by the wave to reach the other end is ______.
Two uniform strings ‘A’ and ‘B’ made of steel are made to vibrate under same tension. If the first overtone of ‘A’ is equal to second overtone of ‘B’ and radius of ‘A’ is twice that of ‘B’. Then the ratio of length of string ‘A’ to that of ‘B’ is ______.
