# Resonance

Resonance is a phenomenon that occurs when the matching vibrations of another object increase the amplitude of an object’s oscillations. This article will explore some examples of resonance and understand the resonant frequency and its calculation.

## What is Resonance?

Objects, mechanical systems and charged particles tend to vibrate at a specific frequency. We call this frequency the resonant frequency or the natural frequency. When a light or a sound wave strikes an object that is already vibrating at some particular frequency, and if that frequency happens to match the resonant frequency of the object it’s hitting; then you’ll get what’s called resonance. Resonance occurs when the matching vibrations of another object increase the amplitude of an object’s oscillations.

Resonance in physics is defined as follows:

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.

The concept of resonance would be hard to comprehend without examples. So, let’s explore the concept of resonance further in the context of some examples.

### Resonance Examples

Some real life examples of resonance that we witness are:

### Musical Instruments

Whenever a 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. Suppose a second interconnected object or instrument vibrates or oscillates at that specified frequency. In that case, 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

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 swing’s timing, which results in the swing’s motion having increased amplitude to reach higher. Once the swing reaches its natural oscillation frequency, a gentle push helps 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 often asked to break their steps 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, which then led to its destruction.

## How to Calculate Resonant Frequency?

Resonant frequency is the natural frequency where a medium vibrates at the highest amplitude. Resonant frequency is usually denoted as f0. Resonance is witnessed in objects 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,

 $$\begin{array}{l}v = λf\end{array}$$

Where v is the wave velocity and 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:

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

Where m is the mass of the spring and 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

$$\begin{array}{l}\omega =\frac{1}{\sqrt{LC}}\end{array}$$

$$\begin{array}{l}\omega =2\pi f\end{array}$$
Where f is the frequency of the resonance, L is the inductance and C is the capacitance.

## Frequently Asked Questions – FAQs

### What is resonance in Physics?

Resonance in physics is 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.

### What are some examples of resonance?

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 swing’s timing, which results in the motion of the swing having increased amplitude to reach higher. Once the swing reaches its natural frequency of oscillation, a gentle push to the swing helps maintain its amplitude due to resonance.

### What causes resonance to occur?

Resonance occurs when the matching vibrations of another object increase the amplitude of an object’s oscillations

### What is the resonant frequency?

The resonant frequency is the natural frequency where a medium vibrates at the highest amplitude.

### How can a bridge collapse due to resonance?

Group of soldiers marching on the bridge are often asked to break their steps 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.

Read more about sound resonance and parallel resonance and learn how it is valid in practical life only through BYJU’S engaging videos.

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