Advertisements
Advertisements
प्रश्न
A pipe closed at one end can produce overtones at frequencies 640 Hz, 896 Hz, and 1152 Hz. Calculate the fundamental frequency.
Advertisements
उत्तर १
The difference between the given overtone frequencies is 256 Hz. This implies that they are overtones that follow one another. Let nc represent the fundamental frequency of the closed pipe and nq, nq-1 represent the frequencies of the qth, (q + 1)th and (q + 2)th consecutive overtones, where q is an integer.
Data: nq = 640 Hz, nq-1 = 896 Hz, nq+2 = 1152 Hz Since only odd harmonics exist as overtones,,
nq = (2q + 1) nc
and nq+1 = [2(q + 1) + 1] nc = (2q + 3) nc
∴ `("n"_("q+1")/("n"_"q"))=(2"q" +3)/(2"q"+1)=896/640=7/5`
∴ `(2"q" + 3)/(2"q"+1)=7/5`
∴ 7(2q + 1) = 5(2q + 3)
∴ 14q + 7 = 10q + 15
∴ 4q = 8
∴ q = 2
As a result, the second, third, and fourth overtones, i.e. the fifth, seventh, and ninth harmonics, correspond to the three stated frequencies.
∴ 5nc = 640 ∴ bc = 128 Hz
उत्तर २
Given: Let frequency for pth overtones
∴ (2p - 1)n = 640 ...(1)
(2p + 1)n = 896 ...(2)
(2p + 3)n = 1152 ...(3)
To find: n = ?
Subtracting (1) from (2)
(2p + 1)n - (2p - 1)n = 896 - 640
2p.n + n - 2pn + n = 256
2n = 128 Hz
Also, subtracting equation (2) from equation (3)
(2p + 3)n - (2p + 1)n = 1152 - 896
n(2p + 3 - 2p - 1) = 256
∴ 2n = 256
∴ n = 128 Hz
APPEARS IN
संबंधित प्रश्न
A string 1m long is fixed at one end. The other end is moved up and down with frequency of 15 Hz. Due to this, a stationary wave with four complete loops gets produced on the string. Find the speed of the progressive wave which produces the stationary wave.
[Hint: Remember that the moving end is an antinode.]
A violin string vibrates with fundamental frequency of 440Hz. What are the frequencies of the first and second overtones?
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 ____________.
When open pipe is closed from one end third overtone of closed pipe is higher in frequency by 150 Hz, then second overtone of open pipe. The fundamental frequency of open end pipe will be ____________.
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 ______.
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 ________.
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 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 ______.
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 stretched uniform wire of length L under tension T is vibrating with frequency 'n' . A closed pipe of same length is also vibrating with same fundamental frequency 'n'. If T is increased by 16 N, it is in resonance with 2nd harmonic of same closed pipe. The initial tension in the wire is ______.
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, ____________.
An organ pipe open at one end is vibrating in first overtone and is in resonance with another pipe open at both ends vibrating in third harmonic. The ratio of lengths of the two pipes is ____________.
In melde's experiment, when the tension decreases by 0.009 kg-wt, the number of loops changes from 4 to 5. The initial tension is ______.
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 ______.
When source of sound moves towards a stationary observer, the wavelength of sound received by him ______.
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 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 ______.
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 ______.
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.
Prove that for pipe closed at one end, the end correction is `e = (n_2l_2-n_1l_1)/(n_1-n_2)`
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.)
