Advertisements
Advertisements
Question
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
Solution
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
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 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)
A violin string vibrates with fundamental frequency of 440Hz. What are the frequencies of the first and second overtones?
The integral multiple of fundamental frequencies are ______
What are harmonics?
A violin string vibrates with the fundamental frequency of 510 Hz. What is the frequency of the first overtone?
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 ____________.
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 ______.
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 ____________
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 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)
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 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)
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 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)
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 ______.
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 ______.
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 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 ______.
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?
Prove that for pipe closed at one end, the end correction is `e = (n_2l_2-n_1l_1)/(n_1-n_2)`
Two consecutive harmonics of air column in a pipe closed at one end are frequencies 150 Hz and 250 Hz. Calculate the fundamental frequency.
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 ______.
