Longitudinal Waves: Definition, Diagram, Examples & Properties

Introduction

Waves are all around us. We hear sound every day. We feel vibrations in the ground. These are all types of waves.

There are two main kinds of waves. One is the transverse wave. The other is the longitudinal wave.

In this article, we will learn all about longitudinal waves. We will look at what they are, how they work, their parts, their speed, and their uses.

By the end, you will understand longitudinal waves clearly and simply.

What Is a Longitudinal Wave?

Definition of a Longitudinal Wave

Sound is the most common example. When you clap your hands, air particles push together and pull apart. This creates a longitudinal wave. In fact, about 99% of the sounds we hear every day travel as longitudinal compressional waves through air.

How Longitudinal Waves Work

Think of a slinky toy. If you push one end forward — applying a force as described by Newton’s first law of motion — a pulse moves through the coils. The coils bunch up in some places. They spread out in other places.

This is exactly how a longitudinal wave works:

• Energy moves from one end to the other
• Each coil only moves a small distance back and forth
• It does not travel with the wave
• Only the energy moves forward

Why They Are Called Longitudinal Waves

The word “longitudinal” means “along the length.” In these waves, the particles move along the same line as the wave itself. That is why they have this name.

If a wave moves to the right, the particles also vibrate to the right and left. They move in the same direction as the wave. This is what makes longitudinal and compressional waves different from transverse waves, where particles move at right angles to the wave.

Labeled Diagram of a Longitudinal Wave

A longitudinal wave diagram helps us see the parts of the wave clearly. In a labeled picture, you can spot two main regions.

Compression

A compression is the part where particles are pushed close together. The particles are packed tightly. The pressure here is high. In a longitudinal wave picture, compressions look like crowded areas.

In sound waves, the air pressure in a compression can be about 0.00002 pascals above normal at the threshold of hearing. Louder sounds create stronger compressions.

Rarefaction

A rarefaction is the opposite. Here, the particles are spread far apart. The pressure is low. In a longitudinal wave labeled diagram, rarefactions look like stretched-out areas.

Direction of Wave Propagation

The wave moves in one direction. This is called the direction of propagation. In a longitudinal wave diagram, an arrow shows this direction. The energy travels this way, from the source outward.

Particle Motion

The particles vibrate back and forth. They move parallel to the wave direction. They do not travel with the wave. They just shake in place. A labeled diagram shows small arrows on the particles going left and right.

Characteristics of Longitudinal Waves

Longitudinal waves have several key features. Let us look at each one.

Particle Motion

Particles in a longitudinal wave move parallel to the wave direction. They vibrate back and forth around a fixed point. This fixed point is called the rest position.

Compressions and Rarefactions

Every longitudinal compressional wave has compressions and rarefactions. Compressions are high-pressure areas. Rarefactions are low-pressure areas. They repeat in a pattern as the wave moves.

Wavelength

The wavelength is the distance between two compressions in a row. Or it is the distance between two rarefactions in a row. It is measured in meters.

For example, a sound with a frequency of 440 Hz (the musical note A) has a wavelength of about 0.78 meters in air at room temperature.

Frequency

Frequency tells us how many waves pass a point in one second. It is measured in Hertz (Hz). A sound of 1000 Hz means 1000 waves pass by every second.

• Humans can hear sounds from about 20 Hz to 20,000 Hz
• Dogs can hear up to about 65,000 Hz

Amplitude

Amplitude is the maximum distance a particle moves from its rest position. A bigger amplitude means a louder sound or a stronger wave. A whisper has a small amplitude. A shout has a large amplitude.

Period

The period is the time for one full wave to pass a point. It is measured in seconds. The period and frequency are related. If the frequency is 500 Hz, the period is 1 ÷ 500 = 0.002 seconds.

Wave Speed

Wave speed tells us how fast the wave moves through a medium. Sound in air at 20°C moves at about 343 meters per second. That is about 1,235 km per hour.

The Wave Equation

Formula (v = fλ)

The wave equation connects speed, frequency, and wavelength:

Where:

• v = wave speed (m/s)
• f = frequency (Hz)
• λ (lambda) = wavelength (m)

Rearranging the Formula

You can rearrange this formula to find any value:

• To find frequency: f = v ÷ λ
• To find wavelength: λ = v ÷ f

SI Units

Sample Calculation

How Energy Travels in Longitudinal Waves

Energy Transfer

A longitudinal wave carries energy from one place to another. The source gives energy to the wave. The wave passes that energy through the medium.

For example, a drum hit sends energy through the air. That energy reaches your ear. You hear the sound. A loud rock concert can produce sound energy of about 1 to 100 watts.

Motion of Particles

The particles in the medium do not travel with the wave. They only vibrate back and forth — each particle has inertia and resists being moved from its rest position. Think of a row of dominoes. Each one pushes the next. But no single domino travels the full distance.

Medium vs Energy Movement

The medium stays in place. Only the energy moves forward. Air does not blow from a speaker to your ear. The air particles just push and pull their neighbors. The energy passes along, like a chain reaction.

Speed of Longitudinal Waves

Factors Affecting Wave Speed

The speed of a longitudinal wave depends on two things:

1. Elasticity of the medium — how quickly it bounces back
2. Density of the medium — how heavy the particles are

A stiffer material lets waves move faster. A denser material slows them down.

Speed in Different Media

Why Sound Travels Fastest in Solids

Solid particles are very close together. They can pass vibrations quickly. They are also more elastic — they return to shape fast. So the wave moves through them at high speed.

Measuring the Speed of Sound

Experimental Methods

There are simple ways to measure the speed of sound:

Method 1: Echo Method. Stand about 50 meters from a wall. Clap your hands. Measure the time for the echo to come back. Use the formula: speed = 2 × distance ÷ time.

Method 2: Two Microphones. Place two microphones a known distance apart. Make a sharp sound. A computer records the time difference. Then calculate the speed.

In 1986, scientists measured the speed of sound in dry air at 0°C as exactly 331.3 m/s. This value is used as a standard today.

Factors Affecting Accuracy

Several things can affect your results:

• Temperature — sound moves about 0.6 m/s faster for every 1°C rise in temperature
• Wind — wind can carry sound faster or slow it down
• Human reaction time — using a stopwatch adds error; electronic timers are better

Sound as a Longitudinal Wave

How Sound Is Produced

Sound is made when something vibrates. A guitar string vibrates. A bell shakes. Your vocal cords move back and forth. These vibrations push and pull the air around them. This is what makes a sound wave, which is a longitudinal wave.

A human voice box vibrates at about 85–255 Hz during normal speech.

How Sound Travels

Sound travels as a longitudinal compressional wave through a medium. It needs matter to travel. The vibrating source pushes air particles. Those particles push the next ones. A pattern of compressions and rarefactions moves through the air.

A sound wave is longitudinal because the air particles vibrate in the same direction as the wave moves.

Can Sound Travel in a Vacuum?

Pressure Waves

What Are Pressure Waves?

A pressure wave is a wave where the pressure changes from high to low in a pattern. Longitudinal waves create pressure waves. The compressions have high pressure. The rarefactions have low pressure.

Relationship Between Pressure Waves and Sound

Sound is a pressure wave. When you speak, you create tiny changes in air pressure. These changes move outward from your mouth. Your ear detects these pressure changes. Your brain reads them as sound.

Normal conversation creates pressure changes of about 0.02 pascals. This is very tiny compared to normal air pressure, which is about 101,325 pascals.

Examples of Longitudinal Waves

Here are the most common examples of longitudinal waves in real life.

Sound Waves

Sound is the best-known longitudinal wave. It moves through air, water, and solids. The particles vibrate back and forth. This creates compressions and rarefactions. We hear sound every day, from talking to music to thunder.

Seismic P-Waves

P-waves are longitudinal waves inside the Earth. The “P” stands for “primary.” They are the fastest seismic waves. They arrive first during an earthquake. P-waves can travel at about 5–8 km/s through the Earth’s crust.

Ultrasound

Ultrasound waves have frequencies above 20,000 Hz. Humans cannot hear them. Doctors use ultrasound to see babies inside the womb. The waves bounce off tissues and create an image. Medical ultrasound uses frequencies between 2 and 18 MHz.

Infrasound

Infrasound waves have frequencies below 20 Hz. They are too low for humans to hear. Elephants use infrasound to talk to each other over distances of up to 10 km. Volcanoes and earthquakes also produce infrasound.

Compression Waves in a Spring (Slinky)

A slinky is a great tool to show longitudinal waves. Push one end of the slinky. The coils bunch up and spread out. You can see the compressions and rarefactions clearly. This is why teachers use slinkies to explain longitudinal and compressional waves in science class.

Seismic Waves

Earthquakes produce waves that travel through the Earth. These are called seismic waves. There are two main types.

P-Waves

P-waves are longitudinal waves. The particles move back and forth in the same direction as the wave. P-waves are the fastest seismic waves. They travel about 6 km/s through rock. They can move through solids, liquids, and gases. They arrive first at seismograph stations.

S-Waves

S-waves are transverse waves. The particles move up and down or side to side. S-waves are slower. They travel about 3.5 km/s through rock. They can only move through solids. They cannot pass through liquid. This is how scientists know that the Earth’s outer core is liquid.

Key Differences

Longitudinal vs Transverse Waves

Differences in Particle Motion

• In a longitudinal wave, particles move parallel to the wave direction — they go back and forth
• In a transverse wave, particles move perpendicular to the wave direction — they go up and down

Comparison Table

Which Waves Can Be Polarized?

Only transverse waves can be polarized. Polarization means the wave vibrates in just one direction. Since longitudinal waves vibrate back and forth along the wave direction, they cannot be polarized.

Real-Life Applications of Longitudinal Waves

Medical Ultrasound

Doctors use ultrasound to see inside the body. Ultrasound waves bounce off organs and tissues. A computer turns the echoes into a picture. This is safe and painless. Over 25 million ultrasound scans are done each year in the United States alone.

SONAR

SONAR stands for Sound Navigation and Ranging. Ships send sound waves into the water. The waves bounce off the ocean floor or objects. The time for the echo helps find the distance. Submarines use SONAR to detect objects up to 100 km away in deep water.

Earthquake Detection

Seismographs detect P-waves from earthquakes. P-waves are longitudinal waves that travel through the Earth. By measuring how long P-waves take to arrive at different stations, scientists can locate where an earthquake started. There are over 4,000 seismograph stations around the world.

Industrial Testing

Engineers use ultrasound to check for cracks in metal and pipes. This is called non-destructive testing (NDT). The sound waves travel through the material. If there is a crack, the wave bounces back differently. This keeps bridges, planes, and buildings safe.

Underwater Communication

Sound travels well in water. Whales and dolphins use longitudinal sound waves to communicate underwater. Blue whales can send sounds across the ocean over distances of more than 1,600 km. The military also uses low-frequency sound to send messages between submarines.

Solved Examples

Finding Wave Speed

Finding Frequency

Finding Wavelength

Speed of Sound Problem

Common Mistakes and Misconceptions

Longitudinal vs Transverse Waves

Many students mix up these two types. Remember: longitudinal = parallel motion. Transverse = perpendicular motion. Sound is longitudinal. Light is transverse.

Compression vs Rarefaction

Some students confuse these parts of a longitudinal wave:

• Compression = particles close together (high pressure)
• Rarefaction = particles far apart (low pressure)

Think of it this way: compression = crowd, rarefaction = space.

Particle Motion vs Wave Motion

Key Takeaways

Conclusion

Longitudinal waves are an important part of science. They are waves where particles move back and forth in the same direction as the wave. Sound is the most common example of a longitudinal wave.

We learned that every longitudinal wave has compressions and rarefactions. The wave equation v = f × λ connects speed, frequency, and wavelength. We also saw that sound travels fastest in solids (about 5,960 m/s in steel) and slowest in gases (about 343 m/s in air).

Examples of longitudinal waves include sound waves, seismic P-waves, ultrasound, and infrasound. These waves have many real-life uses. Doctors use them to see inside the body. Ships use them to find objects in the ocean. Scientists use them to study earthquakes.

Understanding longitudinal waves helps us make sense of the world around us. From the music we enjoy to the earthquakes we study, these waves play a big role in our daily lives.

The Scientists Behind Wave Theory

Frequently Asked Questions