Advertisements
Advertisements
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.]
Advertisements
उत्तर
Data: L = 1 m, n = 15 Hz.
Only one end of the string is fixed. As a result, at the free end, an antinode will form. Hence, with four and a half loops on the string, the string length is
L = `λ/4+4(λ/2)=9/4λ`
∴ λ = `("4L")/9=4/9xx1=4/9`m
v = n λ
∴ Speed of the progressive wave
v = `15xx4/9=60/9` = 6.667 m/s
APPEARS IN
संबंधित 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)
What are harmonics?
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 ______.
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 uniform rope of mass 6 kg hangs vertically from a rigid support. A block of mass 2 kg is attached to the free end of the rope. A transverse pulse of wavelength 0.06 m is produced at the lower end of the rope. The wavelength of the pulse, when it reaches the top is ______. (in m)
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 ____________
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 ____________.
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 ______.
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 ______
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 ______
The air column in an organ pipe closed at one end is made to vibrate so that there are 2 nodes and antinodes each. The mode of vibration is called ______
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 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.
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.
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?
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.)
There are two organ pipes of the same length and the same material but of different radii. When they are emitting fundamental notes.
End correction at open end for air column in a pipe of length ‘l’ is ‘e’. For its second overtone of a closed pipe the wavelength of the wave 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 ______.
