Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
What are harmonics?
Distinguish between an overtone and harmonic.
In a fundamental mode the time required for the sound wave to reach upto the closed end of a pipe filled with air is 't' second. The frequency of vibration of air column is ________.
If length of a closed organ pipe is 60 cm and velocity of sound is 360 m/s, then the frequency of 1st overtone is ____________.
Two strings A and B of same material are stretched by same tension. The radius of the string A is double the radius of string B. Transverse wave travels on string A with speed 'VA' and on string B with speed 'VB'. The ratio `"V"_"A"/"V"_"B"` is ______.
An air column, closed at one end and open at the other resonates with a tuning fork of frequency v, when its length is 45 cm, 99 cm and at two other lengths in between these values. The wavelength of sound in air column is ____________.
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 ____________.
A pipe closed at one end produces a fundamental note of 412 Hz. It is cut into two pieces of equal length. The fundamental notes produced by the two pieces are ____________
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 ______.
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 ______.
If we study the vibration of a pipe open at both ends, then which of the following statements is not true?
The simplest mode of a vibration of the string is called ____________.
A tuning fork with frequency 800 Hz produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Successive resonances are observed at lengths 9.75 cm, 31.25 cm and 52.75 cm. The speed of sound in air is, ____________.
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)
When source of sound moves towards a stationary observer, the wavelength of sound received by him ______.
A pipe closed at one end has length 83 cm. The number of possible natural oscillations of air column whose frequencies lie below 1000 Hz are ______. (velocity of sound in air = 332 m/s)
Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of the first wire is the twice the radius of the second wire, then the ratio of the lengths of the first wire to second wire 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 ______.
An organ pipe closed at one end resonates with a tuning fork of frequencies 180 Hz and 300 Hz. It will also resonate with tuning fork of frequency ______.
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`.
Prove that for pipe closed at one end, the end correction is `e = (n_2l_2-n_1l_1)/(n_1-n_2)`
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?
A pipe closed at one end vibrating in fifth overtone is in unison with open pipe vibrating in its fifth overtone. The ratio of lc : lo is [lc = vibrating length of closed pipe, lo = vibrating length of open pipe]:
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 ______.
