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
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.
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?
What are overtones?
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.
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 ______.
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 ____________.
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 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 ______.
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 ______.
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 equation of vibration of a stretched string fixed at both ends and vibrating in 5th harmonic is Y = 3 sin(0.4x) cos(200πt) where 'x' and 'Y' are in cm and t in second. The length of the string is ______
If the length and diameter of a wire are decreased, then for the same tension the natural frequency of stretched wire will ______.
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)
When source of sound moves towards a stationary observer, the wavelength of sound received by him ______.
The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three beats. The length of open pipe is made `1/3` rd and closed pipe is made three times the original, the number of beats produced will be ______.
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 ______.
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.
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 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 ______.
