 # Resonance

We hear the word “resonance” used a lot in physics, but let us take a second to ask “What is Resonance?” In order to explain the word, we first need to be thorough with the following terms:

• PeriodThe amount of time it takes to complete one cycle.
• Frequency – The number of cycles in one second is the frequency of oscillation.

Now that we have briefed you with the Period and Frequency, let us understand resonance in the next section.

## What is Resonance?

Resonance occurs when a material oscillates at a high amplitude at a specific frequency. We call this frequency resonant frequency. The dictionary defines resonance as,

“the state of a system in which an abnormally large vibration is produced in response to an external stimulus, occurring when the frequency of the stimulus is the same, or nearly the same, as the natural vibration frequency of the system.”

Physics defines Resonance as

A phenomenon in which an external force or a vibrating system forces another system around it to vibrate with greater amplitude at a specified frequency of operation.

## Some Examples of Resonance

Below we have listed examples of resonance that we can witness in our daily lives:

### Musical Instruments

The best examples of resonance can be observed in various musical instruments around us. Whenever any person hits, strikes, strums, drums or tweaks any musical instrument, the instrument is set into oscillation or vibration at the natural frequency of vibration of the instrument. A unique standing wave pattern defines each frequency of vibration as a specific instrument. These natural frequencies of a musical instrument are known widely as the harmonics of the specified instrument. If a second interconnected object or instrument vibrates or oscillates at that specified frequency then the first object can be forced to vibrate at a frequency higher than its natural harmonic frequency. This phenomenon is known as resonance i.e. one object vibrating or oscillating at the natural frequency of another object forces the other object to vibrate at a frequency higher than its natural frequency.

### Swing

One of the familiar examples of resonance is the swing. It is common knowledge that the swing moves forward and backwards when pushed. If a series of regular pushes are given to the swing, its motion can be built. The person pushing the swing has to sync with the timing of the swing. This results in the motion of the swing to have increased amplitude so as to reach higher. Once when the swing reaches its natural frequency of oscillation, a gentle push to the swing helps to maintain its amplitude due to resonance. But, if the push given is irregular, the swing will hardly vibrate, and this out-of-sync motion will never lead to resonance, and the swing will not go higher.

### Bridge

Group of soldiers marching on the bridge are asked to break their steps very often because their rhythmic marching can set extreme vibrations at the bridge’s natural frequency. The bridge can break apart if the synchronized footsteps resonate with the natural frequency of the bridge. One of the examples of the above is the Tacoma Bridge Collapse, where the frequency of the air matched with the frequency of the bridge leading to its destruction.

## How to Calculate Resonant Frequency?

A resonant frequency is the natural vibrating frequency of an object and is usually denoted as f with a subscript zero (f0). Resonance is witnessed in objects that is in equilibrium with acting forces and could keep vibrating for a long time under perfect conditions.

To find the resonant frequency of a single continuous wave, we use the formula,

 $v = λf$

Where,

• v is the wave velocity
• λ is the distance of the wavelength

## Different Types of Resonance

There are many types of resonance, and they are:

### Mechanical Resonance

Mechanical resonance can be defined as the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system’s natural frequency of vibration (its resonance frequency or resonant frequency) than it does at other frequencies.The resonant frequency of a spring is calculated using the given formula:

 $f_{0} = (\frac{1}{2\pi }\times \sqrt{\frac{k}{m}})$

Where,

• m is the mass of the spring
• k is the spring constant

### Acoustic Resonance

Acoustic resonance is a phenomenon in which an acoustic system amplifies sound waves whose frequency matches one of its own natural frequencies of vibration. Acoustic resonance is an important consideration for instrument builders as most acoustic instruments such as the length of tube in a flute, the strings and body of a violin and the shape of a drum membrane use resonators. Acoustic resonance is also important for hearing.

### Electrical Resonance

In a circuit when the inductive reactance and the capacitive reactance are equal in magnitude electrical resonance occurs. The resonant frequency in an LC circuit is given by the formula Read more about sound resonance and parallel resonance and learn how it is valid in practical life only through BYJU’S engaging videos.