# Relationship between natural frequency and resonance

### Natural Frequency

Sound Waves and Music - Lesson 4 - Resonance and Standing Waves If the amplitudes of the vibrations are large enough and if natural frequency is a set of frequencies that have a whole number mathematical relationship between them;. Jul 12, In the field of mechanical engineering, resonance is an undesired phenomenon. of an exciter and a mass with a force-transmitting medium in-between. From this, the natural frequency can be derived mathematically. Jun 8, The definition of these items are: Natural Frequency: All physical structures have yields some interesting phase relationships as shown in Figure 4. . The human ear can hear sound better between and Hertz.

Damping Damping is the way a system naturally dissipates energy. Think back to the guitar example: Energy is dissipated in the form of friction and sound which causes the string to return to rest after it has been plucked. In the single degree of freedom example covered in the previous section, the mass-spring system m and k would stay in motion forever if there was no damper c present as shown in Figure 5.

The higher the damping, c, the sooner the response of the system decays to zero. The system response amplitude at the resonant frequency is reduced by increased damping. At the resonant frequency, the response of the system can be said to be damping dominated. More information about damping, and how to calculate it, can be found in the Knowledge base article: How to determine damping from a FRF.

Structures in the real world are more complex, and have multiple degrees of freedom MDOF.

As a result, real world structures have many natural frequencies. The structure vibrates differently at each of these natural frequencies. How it moves at a particular frequency is called a mode shape. Each mode shape is unique, with different parts of the aircraft participating in the mode.

### Resonant frequency vs Natural frequency | Physics Forums

Left — Lower frequency global mode of aircraft, Right — Higher frequency local mode of aircraft tail. The sound could be musical or it could be noisy; but regardless of its quality, the sound wave is created by a vibrating object. Nearly all objects, when hit or struck or plucked or strummed or somehow disturbed, will vibrate.

If you drop a meter stick or pencil on the floor, it will begin to vibrate. If you pluck a guitar string, it will begin to vibrate.

If you blow over the top of a pop bottle, the air inside will vibrate. When each of these objects vibrates, they tend to vibrate at a particular frequency or a set of frequencies. The frequency or frequencies at which an object tends to vibrate with when hit, struck, plucked, strummed or somehow disturbed is known as the natural frequency of the object.

If the amplitudes of the vibrations are large enough and if natural frequency is within the human frequency rangethen the vibrating object will produce sound waves that are audible. All objects have a natural frequency or set of frequencies at which they vibrate. The quality or timbre of the sound produced by a vibrating object is dependent upon the natural frequencies of the sound waves produced by the objects. Some objects tend to vibrate at a single frequency and they are often said to produce a pure tone.

### Natural Frequency and Resonance - Siemens PLM Community

A flute tends to vibrate at a single frequency, producing a very pure tone. Other objects vibrate and produce more complex waves with a set of frequencies that have a whole number mathematical relationship between them; these are said to produce a rich sound. A tuba tends to vibrate at a set of frequencies that are mathematically related by whole number ratios; it produces a rich tone.

Still other objects will vibrate at a set of multiple frequencies that have no simple mathematical relationship between them. These objects are not musical at all and the sounds that they create could be described as noise. When a meter stick or pencil is dropped on the floor, it vibrates with a number of frequencies, producing a complex sound wave that is clanky and noisy. Factors Affecting the Natural Frequency The actual frequency at which an object will vibrate at is determined by a variety of factors.

Each of these factors will either affect the wavelength or the speed of the object. The role of a musician is to control these variables in order to produce a given frequency from the instrument that is being played. Consider a guitar as an example. There are six strings, each having a different linear density the wider strings are more dense on a per meter basisa different tension which is controllable by the guitaristand a different length also controllable by the guitarist.

The speed at which waves move through the strings is dependent upon the properties of the medium - in this case the tightness tension of the string and the linear density of the strings. Avoiding resonance disasters is a major concern in every building, tower, and bridge construction project.

• Forced Vibrations & Resonance
• Resonant frequency vs Natural frequency

As a countermeasure, shock mounts can be installed to absorb resonant frequencies and thus dissipate the absorbed energy. The Taipei building relies on a tonne pendulum short-ton —a tuned mass damper —to cancel resonance.

Furthermore, the structure is designed to resonate at a frequency that does not typically occur. Buildings in seismic zones are often constructed to take into account the oscillating frequencies of expected ground motion. In addition, engineers designing objects having engines must ensure that the mechanical resonant frequencies of the component parts do not match driving vibrational frequencies of the motors or other strongly oscillating parts. Clocks keep time by mechanical resonance in a balance wheelpendulumor quartz crystal.

The cadence of runners has been hypothesized to be energetically favorable due to resonance between the elastic energy stored in the lower limb and the mass of the runner. This is the source of many percussive sounds we hear.

Acoustic resonance is an important consideration for instrument builders, as most acoustic instruments use resonatorssuch as the strings and body of a violinthe length of tube in a fluteand the shape of, and tension on, a drum membrane.

Like mechanical resonance, acoustic resonance can result in catastrophic failure of the object at resonance. The classic example of this is breaking a wine glass with sound at the precise resonant frequency of the glass, although this is difficult in practice. Electrical resonance Animation illustrating electrical resonance in a tuned circuitconsisting of a capacitor C and an inductor L connected together.

Charge flows back and forth between the capacitor plates through the inductor.

## Natural Frequency

Energy oscillates back and forth between the capacitor's electric field E and the inductor's magnetic field B. Electrical resonance occurs in an electric circuit at a particular resonant frequency when the impedance of the circuit is at a minimum in a series circuit or at maximum in a parallel circuit or when the transfer function is at a maximum. Resonance in circuits are used for both transmitting and receiving wireless communications such as television, cell phones and radio.

Optical cavity An optical cavityalso called an optical resonator, is an arrangement of mirrors that forms a standing wave cavity resonator for light waves. Optical cavities are a major component of laserssurrounding the gain medium and providing feedback of the laser light. They are also used in optical parametric oscillators and some interferometers.