Introduction to Waves – Definition, Types, Properties

A wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities in physics, mathematics, and related subjects, commonly described by a wave equation.

At least two field quantities in the wave medium are involved in physical waves. Periodic waves occur when variables oscillate periodically around an equilibrium (resting) value at a specific frequency.

A traveling wave occurs when the entire waveform moves in one direction; a standing wave occurs when two superimposed periodic waves move in opposite directions. The amplitude of vibration in a standing wave features nulls at some points when the wave amplitude seems reduced or even zero.

Wave

A wave is a disturbance in a medium that transports energy without causing net particle movement. Elastic deformation, pressure variations, electric or magnetic intensity, electric potential, or temperature variations are all examples.

Pictorial representation of waves.

Characteristics of Waves

Waves include the following characteristics:

• The particles of the medium traversed by a wave vibrate only slightly about their mean positions, but they are not permanently displaced in the wave’s propagation direction.
• Along with or perpendicular to the wave’s line of travel, each succeeding particle of the medium performs a motion quite identical to its predecessors.
• During wave motion, only energy is transferred, but not a piece of the medium.

Types of Waves

The several forms of waves are listed here:

1. Transverse Waves:

Waves in which the medium moves at an angle to the wave’s direction.

Examples of transverse waves:

• Water waves (ripples of gravity waves, not sound through water)
• Light waves
• S-wave earthquake waves
• Stringed instruments
• Torsion wave

A crest is the highest point of a transverse wave. It’s a trough at the bottom.

2. Longitudinal Wave:

The movement of the particles in the medium in a longitudinal wave is in the same dimension as the wave’s movement direction.

Examples of longitudinal waves:

• Sound waves
• P-type earthquake waves
• Compression wave

Parts of longitudinal waves:

1. Compression-The particles are close together in this case.
2. Rarefaction-Where the particles are dispersed

3. Electromagnetic Waves:

These are waves that are produced and propagated without the use of a material medium, i.e., they can pass through vacuum and any other material medium.

 Examples of electromagnetic waves:

• visible light
• ultra-violet light
• radio waves
• microwaves

Electromagnetic waves.

4. Mechanical waves:

Only a material medium can produce or propagate mechanical waves. Newton’s equations of motion apply to these waves.

 Examples of mechanical waves:

• waves on water surface
• waves on strings
• sound waves

Mechanical waves are of two types:

1. Transverse wave motion- The particles of the medium vibrate at right angles to the wave’s propagation direction in transverse waves. Transverse waves include string waves, surface water waves, and electromagnetic waves. The disturbance that travels in electromagnetic waves (which include light waves) is caused by the oscillation of electric and magnetic fields at right angles to the wave’s travel direction.
2. Longitudinal wave motion- Particles in the medium vibrate back and forth around their mean location along the energy propagation direction in these sorts of waves. They’re also known as pressure waves. Longitudinal mechanical waves are what sound waves are.

5. Matter waves:

These waves are linked to the movement of matter particles.

Examples of matter waves:

• electrons
• protons
• neutrons

Formula for Speed of Wave  

It’s the entire distance a wave travels in a particular amount of time. The formula for calculating wave speed is as follows:

Wave Speed = Distance Covered/Time taken

Properties of Waves

The following are the primary characteristics of waves:

• Amplitude – A wave is a form of energy transmission. The amplitude of a wave is its height, which is commonly measured in meters. It is proportional to the quantity of energy transported by a wave.
• Wavelength – A wavelength is a distance between identical locations in adjacent cycles of crests of a wave. In addition, it is measured in meters.
• Period – A wave’s period is the amount of time it takes a particle on a medium to complete one complete vibrational cycle. Because the period is a unit of time, it is measured in seconds or minutes.
• Frequency – The number of waves passing a spot in a certain amount of time is referred to as the frequency of a wave. The hertz (Hz) unit of frequency measures one wave every second.

The frequency’s reciprocal is the period, and vice versa.

Period=1 / Frequency

OR

Frequency = 1 / Period

• Speed – The speed of an object refers to how quickly it moves and is usually stated as the distance traveled divided by the time it takes to travel. The distance traveled by a specific point on the wave (crest) in a given amount of time is referred to as the wave’s speed. A wave’s speed is thus measured in meters per second or m/s.

Check: Properties of Waves

Wave Behavior

Waves exhibit several interesting behaviors when they interact with their environment or other waves.

Here are some of the common wave behaviors:

Reflection: When a wave encounters a barrier, it bounces back in the opposite direction. The angle of incidence (the angle at which the wave strikes the barrier) equals the angle of reflection (the angle at which the wave bounces off). You can see reflection in action when sound waves bounce off a wall and you hear an echo, or when light waves bounce off a mirror and create a reflection.

Refraction: When a wave travels from one medium to another where its speed is different, it bends. This bending is called refraction. The amount of bending depends on the difference in speed between the two mediums.

Refraction is why a straw appears bent when inserted in a glass of water, and why light bends as it enters the atmosphere from space, causing objects to appear slightly displaced.

Diffraction: When a wave encounters an opening or a small obstacle, it bends around the edges and spreads out. Diffraction is why sound waves can bend around corners, and why light waves can spread out from a narrow slit.

Interference: When two waves meet, their crests and troughs can interact with each other, producing either constructive or destructive interference. Constructive interference occurs when the crests of two waves line up, creating a wave with a larger amplitude. Destructive interference occurs when the crest of one wave lines up with the trough of another wave, partially or completely canceling out the waves.

Doppler effect

The Doppler Effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It occurs for any type of wave, but it is commonly observed with sound waves.

Source approaching: Waves compressed, higher perceived frequency (e.g., ambulance siren).

Source moving away: Waves stretched, lower perceived frequency (e.g., ambulance siren moving away). • Applies to all waves:

Sound waves (common experience).

Light waves (astronomical study of stars and galaxies).

Standing Wave

• Standing waves result from the interference of two waves traveling in opposite directions with the same frequency and amplitude.
• Instead of propagating, the energy of these waves becomes confined within a specific region, forming a stationary pattern of oscillation.
• Standing waves have points of minimal displacement called nodes and points of maximal displacement called antinodes.
• They are observed in various physical systems, including vibrating strings, acoustic resonance in pipes, and electromagnetic waves in transmission lines.
• Standing waves play a crucial role in phenomena such as musical instrument vibrations, sound resonance, and the behavior of electromagnetic fields in antennas.

Sample Problems

Problem 1: In a specific medium, a wave travels at 900 meters per second. Calculate the wavelength of a specific point in the medium if 3000 waves pass through it in 2 minutes.

Solution:

The speed of a wave in medium v = 900 ms^-1

Freq. of wave = no. of waves passing per sec (n) = 3000 waves/2 min = 3000 / 2 × 60 = 25 s

Wave length (λ) = ?

v = n × (λ)

λ = v/n

  = 900/25 

  = 36 m

Problem 2: What distinguishes the roar of our national animal from that of a mosquito?

Solution:

The buzzing of a mosquito creates a sound of high pitch and low intensity or loudness, but the roaring of a national animal (tiger) produces a sound of low pitch and high intensity or loudness.

Problem 3: Is it feasible to tell when a vessel maintained beneath the faucet is going to overflow?

Solution:

The length of an air column is inversely related to the frequency of the note it produces. The length of the air column above the vessel reduces as the level of water in the vessel rises. It generates a sound with a decreasing frequency, i.e. the sound gets shorter. It is possible to determine whether the vessel is filled with water based on the shrillness of the sound.

Problem 4: The bottom of a ship in the sea shoots SONAR waves straight down into the saltwater. After 3.5 s, the signal reflects off the deep bottom bedrock and returns to the ship. When the ship reaches 100 km, it transmits another signal, which is received after 2 s. Calculate the depth of the sea in each example, as well as the height difference between the two.

Solution:

Velocity of SONAR waves in water C = 1500 ms^-1

Time taken by be wave after reflection from the bottom of sea

2t = 3.5s

t =1.75s

Distance covered (d) = ?

C = d/t => d = c.t = 1500 × 1.75 – 2625 m

After moving 100km

The time taken by the wave = 2t = 2s

T  = 2/2 = 1s

d =?

d = 1500 × l

= 1500

The difference between these two heights = 2625 – 1500

= 1125m

Problem 5: Why does a tone sound louder in an empty room than in a room with furniture and other objects?

Solution:

Sound is an energy form. The majority of the energy is absorbed by the furniture that acts as an obstruction. As a result, the strength of sound decreases, yet in an empty room, the intensity of sound remains relatively constant due to the absence of impediments, and we perceive it as louder.

Waves- FAQs

What is a wave?

A wave is a disturbance or oscillation that propagates through a medium or space, transferring energy without transferring matter.

What are the main types of waves?

Waves can be categorized into two main types: mechanical waves, which require a medium to propagate (e.g., sound waves, water waves), and electromagnetic waves, which can travel through a vacuum (e.g., light waves, radio waves).

What are the key characteristics of waves?

Waves exhibit characteristics such as frequency (the number of oscillations per unit time), wavelength (the distance between two consecutive points of similar phase), amplitude (the maximum displacement from the equilibrium position), and speed (the rate at which the wave travels through the medium).

How do waves transfer energy?

Waves transfer energy by causing particles in the medium to oscillate about their equilibrium positions as the wave passes through.

What is the difference between mechanical and electromagnetic waves?

Mechanical waves require a medium to propagate, while electromagnetic waves can travel through a vacuum. Mechanical waves typically involve the motion of particles in the medium, whereas electromagnetic waves consist of oscillating electric and magnetic fields.

What are some common examples of waves in everyday life?

Examples of waves in everyday life include sound waves (e.g., music, speech), water waves (e.g., ocean waves, ripples in a pond), light waves (e.g., sunlight, visible light), and radio waves (e.g., Wi-Fi signals, radio broadcasts).

How are waves used in communication?

Waves, particularly electromagnetic waves such as radio waves and microwaves, are used in various forms of communication, including radio and television broadcasts, cellular and Wi-Fi networks, satellite communications, and radar systems.

What is the relationship between frequency and wavelength in waves?

Frequency and wavelength are inversely proportional in waves, meaning that as the frequency increases, the wavelength decreases, and vice versa. This relationship is described by the wave equation: speed = frequency × wavelength.

How are waves studied and analyzed in science and engineering?

Waves are studied and analyzed using mathematical models and principles of physics, such as wave equations and the principles of wave behavior (e.g., reflection, refraction, interference). Various scientific instruments and technologies, such as oscilloscopes and spectroscopes, are used to measure and analyze wave properties.

What are some phenomena associated with waves?

Wave phenomena include reflection (bouncing back of waves when they encounter a boundary), refraction (bending of waves as they pass from one medium to another), diffraction (bending of waves around obstacles), interference (interaction of waves resulting in the reinforcement or cancellation of wave amplitudes), and resonance (enhancement of wave amplitudes due to the natural frequency of a system).