Advertisements
Advertisements
Question
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)
Advertisements
Solution
Data: Open pipe, n0 = 600 Hz, nc, 1 = n0, 1 (first overtones)
For an open pipe, the fundamental frequency,
n0 = `"v"/("2L"_"0")`
∴ The length of the open pipe is
L0 = `"v"/("2n"_"0")=330/(2xx600)` = 0.275 m
For the open pipe, the frequency of the first overtone is
2n0 = 2 x 600 = 1200 Hz
For the pipe closed at one end, the frequency of the first overtone is `(3"v")/"L"_"0"`
By the data, `"3v"/"4L"` = 1200
∴ LC = `(3xx330)/(4xx1200)` = 0.206 m
The pipe is 27.5 cm in length when open on both ends and 20.6 cm when closed on one end.
APPEARS IN
RELATED QUESTIONS
Answer in brief:
What are harmonics and overtones?
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 ______.
The integral multiple of fundamental frequencies are ______
Distinguish between an overtone and harmonic.
The equation of simple harmonic progressive wave is, y = sin π/2 (4t/0.025 – x/0.25). Where all quantities are in the S.I. system. Find the amplitude, frequency, wavelength, and velocity of the wave.
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 ______.
The fundamental frequency of a closed pipe is 400 Hz. If `1/3`rd pipe !s tilled with water, then the 3 frequency of 2nd harmonic of the pipe will be (neglect and correction).
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 ______.
An organ pipe has a fundamental frequency of 120 Hz. Its fourth overtone is 600 Hz. Find the type of the pipe.
An open pipe of certain length produces fundamental frequency f1. A closed pipe of some other length produces fundamental .frequency f2. When the two are joined to form a longer close tube, its fundamental frequency will be ____________.
A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their pth overtone is ______.
The fundamental frequency of sonometer wire increases by 9 Hz, if its tension is increased by 69%, keeping the length constant. The frequency of the wire is ______.
Transverse waves of the same frequency are generated in two steel wires A and B. The diameter of A is twice that of B and the tension in A is half that in B. The ratio of the velocities of waves in A and B is ____________.
Length of an organ pipe open at both ends is 34 cm. If velocity of sound is 340 m is, then the frequency of 2nd overtone is ______.
A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air colunm in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.
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)
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 ______.
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 ______.
If the end correction of an open pipe is 0.8 cm, then the inner radius of that pipe will be ______.
A stretched string 0.7 m long and fixed at its ends vibrates in the second overtone of frequency 300 Hz. Find the speed of the transverse wave on the string.
How does the fundamental frequency of a vibrating string depend on the radius of the cross-section of the string and the mass density material of the string?
Two wires, each 1 m long and of the same diameter, have densities 8 × 103 kg/m3 and 2 × 103 kg/m3 and are stretched by tensions 196 N and 49 N respectively. Compare their fundamental frequencies.
A sonometer wire is subjected to a certain tension. If the tension is increased four times and the length of wire is reduced to half the original value, how is frequency of vibrations altered?
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.)
