Learn
Games

14.4.2 - Speed of a Longitudinal Wave (Speed of Sound)

Interactive Audio Lesson

Listen to a student-teacher conversation explaining the topic in a relatable way.

Understanding Longitudinal Waves

Unlock Audio Lesson

Signup and Enroll to the course for listening the Audio Lesson

Teacher
Teacher

Today, we're going to discuss longitudinal waves, specifically focusing on sound waves. Can anyone explain what we mean by longitudinal waves?

Student 1
Student 1

I think longitudinal waves are waves where the particles of the medium move in the same direction as the wave.

Teacher
Teacher

Correct! In longitudinal waves, the medium compresses and rarefies. An easy way to remember this is: 'Compression in the direction of sound.' Now, how does this relate to sound?

Student 2
Student 2

Sound travels as compressions and rarefactions in the air.

Teacher
Teacher

Exactly! And these compressions create regions of higher and lower pressure that travel through the medium.

Speed of Sound

Unlock Audio Lesson

Signup and Enroll to the course for listening the Audio Lesson

Teacher
Teacher

Now, let’s talk about the speed of sound specifically. What factors do you think affect how fast sound travels in different media?

Student 3
Student 3

I think it depends on the medium, like whether it’s a solid, liquid, or gas.

Teacher
Teacher

Great point! The speed of sound is determined by the medium's bulk modulus and density. Can anyone define bulk modulus?

Student 4
Student 4

Isn't it the measure of a material's resistance to uniform compression?

Teacher
Teacher

Absolutely! The bulk modulus indicates how much pressure is required to compress the medium, affecting the speed of sound. Now, remember the formula: v = √(B/ρ).

Comparing Sound in Different Media

Unlock Audio Lesson

Signup and Enroll to the course for listening the Audio Lesson

Teacher
Teacher

Can anyone tell me why sound travels faster in solids than in gases?

Student 1
Student 1

Is it because solids are denser than gases?

Teacher
Teacher

Partly right. While solids are typically denser, the crucial factor is that solids have a much higher bulk modulus. This means they transmit compressional waves faster.

Student 2
Student 2

So, if the bulk modulus is high, the sound will travel faster?

Teacher
Teacher

Exactly! That’s a vital point. Sound travels fastest in materials where the bulk modulus is high and density is manageable.

Newton’s and Laplace’s Formulas

Unlock Audio Lesson

Signup and Enroll to the course for listening the Audio Lesson

Teacher
Teacher

Newton developed a formula for the speed of sound in gases but found it underestimated the actual speed. Does anyone know why?

Student 3
Student 3

I think it has to do with how pressure changes in gases when sound travels.

Teacher
Teacher

Correct! The pressure changes are adiabatic, meaning the temperature doesn't remain constant. This is where Laplace's correction comes in. Can someone express this new relation?

Student 4
Student 4

Is it v = √(γP/ρ)?

Teacher
Teacher

Well done! This correction accounts for the adiabatic nature of sound propagation.

Introduction & Overview

Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.

Quick Overview

This section discusses the speed of longitudinal waves, particularly the speed of sound, highlighting how different properties of the medium affect this speed.

Standard

The speed of sound is influenced by the medium's bulk modulus and density, which are crucial in determining how compressions and rarefactions propagate in a fluid. These calculations show that the speed of sound varies in different materials and conditions.

Detailed

In longitudinal waves, such as sound, the medium’s particles oscillate in the same direction as the wave's propagation. The speed of sound, expressed as v = √(B/ρ), is determined by the medium's bulk modulus (B) and its density (ρ). This section elaborates on how different physical properties of solids, liquids, and gases affect the propagation speed of sound. For example, sound travels faster in solids than in gases due to the higher density and greater bulk modulus of solids. Newton’s original formula for the speed of sound in gases is modified with Laplace’s correction to account for the adiabatic processes involved in sound propagation.

Youtube Videos

Class 11th Physics | Speed of Transverse & Longitudinal Wave | Example 14.3 & 14.4 | Chapter 14
Class 11th Physics | Speed of Transverse & Longitudinal Wave | Example 14.3 & 14.4 | Chapter 14
Speed of Longitudinal Waves - Waves | Class 11 Physics Chapter 14 | CBSE 2024-25
Speed of Longitudinal Waves - Waves | Class 11 Physics Chapter 14 | CBSE 2024-25
Newton's formula for speed of sound and Laplace' correction (Derivation)
Newton's formula for speed of sound and Laplace' correction (Derivation)
Speed Of Longitudinal Wave (Hindi) | Class 11 Physics
Speed Of Longitudinal Wave (Hindi) | Class 11 Physics
11th Physics | Chapter 8 | Sound | Lecture 1 | Maharashtra Board | JR Tutorials |
11th Physics | Chapter 8 | Sound | Lecture 1 | Maharashtra Board | JR Tutorials |
Waves11 : Sound Waves 02 - Speed of Sound Waves in Air II Speed of Longitudinal Waves JEE MAINS/NEET
Waves11 : Sound Waves 02 - Speed of Sound Waves in Air II Speed of Longitudinal Waves JEE MAINS/NEET
Longitudinal and Transverse Waves Demonstration
Longitudinal and Transverse Waves Demonstration
SOUND 02 | The Speed of Travelling Wave | Physics | Class11th/MHTCET/JEE/NEET
SOUND 02 | The Speed of Travelling Wave | Physics | Class11th/MHTCET/JEE/NEET
Speed of Longitudinal waves class 11 derivations - waves
Speed of Longitudinal waves class 11 derivations - waves
WAVES in 74 Minutes | FULL Chapter For NEET | PhysicsWallah
WAVES in 74 Minutes | FULL Chapter For NEET | PhysicsWallah

Audio Book

Dive deep into the subject with an immersive audiobook experience.

Understanding Longitudinal Waves

Unlock Audio Book

Signup and Enroll to the course for listening the Audio Book

In a longitudinal wave, the constituents of the medium oscillate forward and backward in the direction of propagation of the wave. We have already seen that the sound waves travel in the form of compressions and rarefactions of small volume elements of air.

Detailed Explanation

Longitudinal waves are characterized by the movement of medium particles in the same direction as the wave itself. When sound travels through air, it generates areas where air molecules are compressed (high pressure) followed by areas where they are spread apart (low pressure). These compressions and rarefactions travel through the air, allowing us to hear sound. It’s like pushing a slinky back and forth, creating waves in the coil. This oscillation is essential to how sound waves propagate.

Examples & Analogies

Think of a crowd in a stadium. When people clap their hands together in rhythm, the sound of clapping travels through the air. The claps create waves of pressure changes in the air, much like compressions in a longitudinal wave, moving from the clapping person to the farthest spectators.

Elastic Properties and Sound Propagation

Unlock Audio Book

Signup and Enroll to the course for listening the Audio Book

The elastic property that determines the stress under compressional strain is the bulk modulus of the medium defined by (see Chapter 8) PB = V/VΔ= −Δ. Here, the change in pressure ∆P produces a volumetric strain V/VΔ. B has the same dimension as pressure and is given in SI units in terms of Pascal (Pa).

Detailed Explanation

The bulk modulus (B) describes how incompressible a substance is. It quantifies the pressure increase required to change the volume of a material by a certain amount. In the context of sound, it relates the pressure fluctuations in a sound wave to the density changes in the air. A larger bulk modulus means sound can travel faster through the medium, as it can withstand compression more effectively.

Examples & Analogies

Imagine squeezing a balloon. The amount of effort you need to compress the balloon relates to how much air inside can resist that squeeze. Likewise, different materials react differently to pressure changes, which affects how sound travels through them.

Speed of Sound in Different Media

Unlock Audio Book

Signup and Enroll to the course for listening the Audio Book

Thus, if B and ρ are considered to be the only relevant physical quantities, v = C B/ρ, where C is the undetermined constant from dimensional analysis. The exact derivation shows that C=1. Thus, the general formula for longitudinal waves in a fluid is: v = B/ρ.

Detailed Explanation

The speed of sound (v) in a medium is determined by both its bulk modulus (B) and its mass density (ρ). A higher bulk modulus indicates that the medium can handle more pressure without changing volume, which allows sound to travel faster. Conversely, a higher density means there are more particles in a given volume, which can slow down the rate at which sound travels. The formula v = B/ρ provides a straightforward way to calculate speed when you know the properties of the medium.

Examples & Analogies

Think about different vehicles. A race car (low density, high power) can accelerate faster than a bus (high density, slower power). Similarly, sound travels faster in materials that are ‘light’ but with high pressure resistance, like metals, compared to heavier gases like carbon dioxide.

Newton’s Formula and Real-Life Application

Unlock Audio Book

Signup and Enroll to the course for listening the Audio Book

For gases, since B = γP, the speed of sound is given by, v = γ/ρP. This relation was first given by Newton and is known as Newton’s formula.

Detailed Explanation

Newton's formula for sound speed applies specifically to gases, where the bulk modulus (B) can be expressed in terms of pressure (P) and the adiabatic index (γ). The relationship identifies how sound travels faster in gases under higher pressure, owing to increased molecular collisions facilitating the wave's propagation. Hence, it derivatively simplifies understanding of sound speed in different thermal conditions.

Examples & Analogies

When you blow up a balloon and then release it, the sound made as it zips around is much faster than a whisper just because of the added pressure inside. That pressure helps sound travel through the gas more effectively, just as the density affects how quickly sound travels overall.

Laplace's Correction

Unlock Audio Book

Signup and Enroll to the course for listening the Audio Book

A modification of Newton’s formula, referred to as the Laplace correction, takes into account that the pressure variations in the propagation of sound waves are so fast that there is little time for heat flow to maintain constant temperature.

Detailed Explanation

The Laplace correction accounts for the fact that sound waves do not propagate isothermally (constant temperature). Instead, because the changes in pressure and density occur rapidly, the process is adiabatic (without heat exchange). This means the speed of sound is actually slightly higher than Newton's initial predictions, giving rise to a more accurate formula for sound speed in gases under varying conditions.

Examples & Analogies

Consider a rapidly collapsing gas canister, used by a foam spray. The noise created is louder than a gentle release of air just because the pressure and temperature inside the canister change rapidly, confirming the necessity of considering quick temperature effects in sound speed calculations.

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Longitudinal Waves: Waves where the medium's particles oscillate in the same direction as the wave.

  • Speed of Sound: A function of the medium's bulk modulus and density, indicating how quickly sound travels.

  • Newton's Formula: The original equation for predicting the speed of sound, later corrected by Laplace.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • Sound travels faster in water than in air due to higher bulk modulus and density.

  • In solids, such as steel, sound travels even faster as they have both high density and high bulk modulus.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎵 Rhymes Time

  • Bulk modulus high, speed goes high, sound will fly, across the sky!

📖 Fascinating Stories

  • Imagine a superhero named Bulk, who compresses air swiftly, propelling sound through it faster than a speeding bullet!

🧠 Other Memory Gems

  • Remember V-Bird for velocity: V = √(B/ρ) - Bulk over density is the key.

🎯 Super Acronyms

SBS - Speed, Bulk, and Sound

  • The three factors determining how fast sound travels.

Flash Cards

Review key concepts with flashcards.

Glossary of Terms

Review the Definitions for terms.

  • Term: Longitudinal Wave

    Definition:

    A wave in which the particles of the medium oscillate parallel to the direction of wave propagation.

  • Term: Bulk Modulus (B)

    Definition:

    A measure of a substance's resistance to uniform compression, defined as the pressure increase needed to decrease the volume of the substance.

  • Term: Speed of Sound (v)

    Definition:

    The distance traveled by a sound wave in a unit of time, which depends on the medium's bulk modulus and density.