Advertisements
Advertisements
Question
Answer in brief:
What are harmonics and overtones?
Solution
A stationary wave is formed in a bounded condition, with the boundary being either rigid support or a free end. The boundary conditions restrict the possible stationary waves and allow only a discrete set of frequencies.
The fundamental frequency of vibration is the lowest allowed frequency, n1. Harmonics are integral multiples of the fundamental frequency. The harmonics may or may not be present in the sound so produced. The first harmonic is defined as the fundamental frequency. The second harmonic is 2n1, which is twice the fundamental, and the third harmonic is 3n1, and so on.
Consider a vibrating string. The modes of vibration are all multiples of the fundamental and are related to the string length and wave velocity. Higher frequencies are found via the relationship fn= nf1, wavelength = `2"L"/"n"` where L is the string length.
An overtone is a name given to any resonant frequency above the fundamental frequency or fundamental tone. The first permitted frequency over the fundamental is termed the first overtone, the next higher frequency is called the second overtone, and so on. The list of successive overtones for an object is called the overtone series. The first overtone as well as all subsequent overtones in the series may or may not be an integer multiple of the fundamental. Sometimes the relationship is that simple, and other times it is more complex, depending on the properties and geometry of the vibrating object.
APPEARS IN
RELATED QUESTIONS
The integral multiple of fundamental frequencies are ______
What are harmonics?
What are overtones?
A violin string vibrates with the fundamental frequency of 510 Hz. What is the frequency of the first overtone?
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 ______.
The fundamental frequency of a closed pipe is 400 Hz. If `1/3`rd pipe !s tilled with water, then the 3 frequency of 2nd harmonic of the pipe will be (neglect and correction).
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 ________.
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 ____________.
A thin wire of 99 cm is fixed at both ends as shown in figure. The wire is kept under a tension and is divided into three segments of lengths l1, l2, and l3 as shown in figure. When the wire is made to vibrate respectively with their fundamental frequencies in the ratio 1:2:3. Then the lengths l1, l2, and l3 of the segments respectively are (in cm).
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 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 ____________.
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 transverse wave propagating along the string is y = 0.3 sin (x + 20t) where x, y are in metre and t in second. The linear density of the string is 1.2 x 10-4 kg/m. The tension in the string 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, ____________.
If the length and diameter of a wire are decreased, then for the same tension the natural frequency of stretched wire will ______.
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 ______
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 ______.
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 ______.
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 ______.
Explain why velocity increases when water flowing in a broad pipe enters a narrower pipe. A sonometer wire, 36 cm long, vibrates with a frequency of 288 Hz in the fundamental mode when it is under a tension of 24.5 N. Calculate the linear density of the material of the wire
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)`
