Resonance – Definition, Types and How to Calculate Resonant Frequency?

Jul 13, 2022

What is Resonance?

All objects tend to vibrate at a specific frequency called the natural or the resonant frequency. So, when a sound or light wave vibrating at a particular frequency strikes such an object, and the frequency matches the resonant frequency of that object, it is called resonance.

When the matching vibrations of an object increase the amplitude of another object’s oscillations, the phenomenon is termed resonance.

Did you know?

it was first studied in acoustical systems like musical instruments and the human voice.

Types of Resonance

If you are not aware of how many types of resonance there are, then you must check it right away! Following are the main categories of it:

Sound Resonance

Vocal cords: The vibrating vocal cords produce sound waves. These are pressure waves composed of alternating rarefactions with a less than average density and compressed sections with a greater than average density.

Musical Instruments: A brass instrument involves the creation of an initial vibration by the player’s lips against the mouthpiece. When the vibration matches the resonant frequency of the pipe the player blows into, there is resonance. The oscillation amplitude increases notably, producing an audible sound.

Woodwind instruments have a reed that vibrates when air passes over them. Resonance and amplification transform this vibration into a musical tone that you hear. String instruments such as guitars have strings with a resonant frequency of vibration. The sound waves resonate in the guitar cavity to produce louder music.

Mechanical Resonance

Bridge: If you have heard of the famous incident of the destruction of the Tacoma Narrows Bridge in 1940, you already know what mechanical resonance is.

Soldiers marching on the bridge are always recommended to break their steps because there is a possibility that their marching might set extreme vibrations. The bridge is at risk of collapsing if the synchronised march resonates with the bridge’s natural frequency, as happened in the case of the Tacoma Bridge Collapse. The frequency of air matched that of the bridge leading to its destruction.

Vehicles and Spacecraft: You must have experienced a buzz or a rattle in your car occurring at a certain speed. It happens because of resonance. Aircraft and surface vehicles are designed such that their engine’s vibrations are at a safe minimum.

Swing: When you push a swing, it does not go high at the first go because the oscillatory motion of the swing has a natural frequency. However, when you learn to apply a periodic force that matches the swing’s natural frequency, the pushing gets much more effective. Once in resonance, the oscillation amplitude of the swing increases and you go higher each time.

Electrical Resonance

Communication devices: It is found to occur in frequency-sensitive AC circuits. It makes it possible for communication devices with AC circuits to accept signals of only specific frequencies, rejecting the others. So, electrical resonance occurs when the inductive reactance and the capacitive reactance are equal in magnitude.

Television and Radio: When the frequency of the TV station or Radio station matches the frequency set in the Radio/TV device, the waves of the same frequency enable the radio to move the vibration in increased amplitude.

Magnetic Resonance

It has also been detected on the nuclear scale. When atoms or nuclei respond to the applied magnetic fields by absorbing or emitting electromagnetic radiation, the phenomenon is termed magnetic resonance. So, in this process, physical excitation or resonance is set up through magnetism. It is also called nuclear magnetic resonance (NMR)

NMR is widely used in various scientific techniques, such as for studying crystals and non-crystalline materials via NMR spectroscopy. It also finds application in medical imaging techniques, such as MRI (Magnetic Resonance Imaging).

Orbital Resonance

Orbital resonance is when two orbiting bodies exert a periodic gravitational influence on one another due to their orbital periods that are related by a ratio of two integers. Orbital resonance enhances the mutual gravitational forces of the bodies. An example is a resonance between Pluto and Neptune in the ratio 2:3.

How to Calculate Resonant Frequency?

The natural frequency at which a medium vibrates with the highest amplitude is called resonant frequency. It is denoted by f0.

The formula for calculating the resonant frequency of a single continuous wave is as follows:

v = λf

v = wave velocity

λ = distance of the wavelength

Calculating Multiple Resonance Frequencies

You can also find multiple resonance frequencies for waves moving at the same time. Use the following formula to calculate the resonance frequency of each vibration:

fn = v/λn = nv/ 2L

In the above formula,

λn is the wavelength of the nth frequency, and

L is the length of the string.

Calculating Resonant Frequency of a Spring

To calculate the resonant frequency of a spring, use the following formula:

f0 = 12 km

In the above formula,

π has a value of 3.14,

m stands for the mass of the spring, and

k is the spring constant.

Example 1: Given the mass of the spring is 2 kg, and 150 N/m is the spring constant. Calculate the resonant frequency of the spring.

Solution: Given

m = 2 kg

k= 150 N/m

Using the resonant frequency formula f0 = 12 km, we can determine f0

f0 = 12 km

f0 = 12 1502

f0 = 12 75

f0 = 12 8.66

f0 = 12 3.14 8.66

f0 = 8.66 ÷ 6.28

f0 = 1.38 Hz

Calculating Resonant Frequency of a Resonant Circuit

What is a resonant circuit? A circuit containing a parallel-connected capacitor and inductor is called a resonant circuit. It is also called a tank circuit or an LC circuit. The frequency of this resonant circuit is called the resonant frequency.

The formula for calculating the resonant frequency of a resonant circuit is as follows:

f0 = 12 LC

In the above formula,

f0 is the resonant frequency in Hz

L is for inductance, and C is for capacitance.

Example 2: The inductance and capacitance of a resonant circuit are 2H and 1F. What is the resonant frequency of the circuit?

Solution: Given

L = 2H

C = 1F

Using the resonant frequency formula f0 = 12 LC, we can determine f0

f0 = 12 21

f0 = 12 2

f0 = 12 1.414

f0 = 18.89

f0 = 0.11 Hz

Why do we Calculate Resonant or Natural Frequencies?

The mode shapes and natural frequencies are amongst the most critical properties of any system. You have come across situations wherein excessive vibrations in a system led to functional and structural issues, for instance, in cars, vehicles, bridges, and more.

The reason behind the occurrence of these issues is a match of the natural frequencies with the resonant frequencies of a system. So, if you employ a time-varying force on a system and choose a frequency that is equivalent to one of the system’s natural frequencies, the result will be immense amplitude vibrations. This situation can pose a risk and put your system in jeopardy.

So, it is important to calculate the natural frequencies before designing a mechanical system to ensure the natural frequencies are greater than the possible excitation frequency your system might encounter.

Conclusion

Once you understand the resonance meaning, you can apply it to various happenings around you in everyday life. For instance, swings in motion, tuning guitars using resonance, and oscillating pendulums are some common examples of resonance.

Frequently Asked Questions

Q1. What conditions are vital for producing resonance?

The conditions vital for resonance production in an object are as follows:

An external vibration force should drive the object.
The natural frequency of the non-vibrating body should be equal to or a multiple of the frequency of the vibrating body.

Q2. How is frequency related to resonance?

In resonance, an increased amplitude occurs when the frequency of externally applied periodic force matches or is close to a natural frequency of the system on which it is applied.