Speed of Sound: How Sound Travels Through Objects and Materials

Posted by Acoustical Surfaces on 03/14/2024 11:54 am | Leave a Comment

From the snap of a twig to the booming echo of a drumbeat, sound plays an important role in helping us navigate our space. While sound is incredibly important, many people rarely stop to ponder its physical properties.

In physics, sound is defined as an acoustic vibration that sends waves through a medium, such as a solid, liquid, or gas.¹ These mediums’ properties can influence sound’s speed. By understanding the relation between material properties and the speed of sound, you can optimize the acoustics of various spaces, from professional recording studios to company conference rooms.

We’ll be diving into the fascinating mechanics of sound propagation and explain how different objects’ density, elasticity, and temperature all influence the speed of sound (plus how to contain or absorb those fast-moving sound waves).

Table of Contents

What is the Formula for the Speed of Sound?

Many people assume that the speed of sound is a constant number, but this isn’t the case. The materials that transmit sound can influence its speed considerably. Even so, there is a general speed of sound formula, which multiplies the sound’s wavelength by its frequency.² In mathematical terms:

v=fλ

In this formula:

v represents the speed of sound
f is the frequency of the sound wave
λ is the length of the sound wave

While this general formula is an excellent baseline, the speed of sound can vary greatly from one medium to the next, depending on its temperature, density, and elasticity.

Speed of Sound: Example Equation

To clarify the connection between the sound’s speed, frequency, and wavelength, let’s take a look at a real-life example.

Let’s say that you’re measuring a sound with a frequency of 261 Hz, also known as middle C or concert pitch.³ This sound’s wavelength is around 1.3 meters. After plugging these numbers into the speed of sound formula, you can calculate sound using the following equation:

v=(261 Hz)(1.3 m)

v=341.9 m/s

With this equation in mind, let’s take a closer look at the role of various materials’ properties on the speed of sound.

How Does a Material’s Density Impact the Speed of Sound?

Density, which measures the mass per unit volume of a given material, can influence the speed of sound significantly. That’s because density dictates how closely a material’s molecules are packed together.

Since sound is kinesthetic energy that travels by passing from one molecule to the next, materials with more densely packed molecules facilitate faster sound propagation. For this reason, sound travels faster through solids than liquids and faster through liquids than gasses.

Varying Densities of Different Elements

Denser elements often feature heavier molecules, which take more energy to vibrate, subsequently slowing down sound’s speed. As a result, sound can travel through aluminum nearly twice as fast as it moves through gold, due to the differences in the molecules.⁴

How Does Material Density Relate to Soundproofing?

If you’re interested in optimizing the acoustics of a space, you’ll likely employ soundproofing solutions at some point. Soundproofing materials add mass to walls and ceilings to prevent sound from escaping.

Since these materials are often quite dense, it begs the question, “Why use dense, solid materials for soundproofing if sound waves travel through them faster?”

When dense materials are thick enough, they contain enough molecules to drain the sound wave of energy before it can reach the other side. That’s why most soundproofing solutions, from double-layer drywall to solid-core doors, are so thick.

How Does a Material’s Elasticity Impact the Speed of Sound?

Another key factor that influences the speed of sound through materials is their elasticity, which refers to a material’s ability to maintain its shape when placed under stress. For example, a rigid material like steel won’t lose its shape as easily as a more flexible material like rubber.

Materials with atoms that are strongly attracted to each other end up being more rigid, due to their powerful internal bonds. The strength of these bonds ultimately determines how quickly a material will return to its original shape.

So, what does this mean for the speed of sound? Particles that quickly regain their shape after an external force will also vibrate at higher speeds. As a result, they enable sound to travel faster than materials with lower elastic properties.⁴

Speed of Sound Elasticity Equation

If you want to flex your mathematical muscles, you can calculate the speed of sound while taking into account different material’s elastic properties.

This more complicated formula divides the elastic property by the inertial property and takes the resulting number’s square root, as showcased by this equation²:

Here’s a quick breakdown:

Elastic property is a material’s ability to deform and reform in the face of an external force.
Inertial property looks at whether a material will stay at rest or in motion in the absence of an external force.

How Does a Material’s Temperature Impact the Speed of Sound?

Many people are often surprised to learn that temperature can influence the speed of sound. Typically, higher temperatures facilitate faster sound travel, especially through gasses.

So, what’s behind this phenomenon? Well, heat is a form of kinetic energy. Increasing the temperature speeds up the vibration of molecules within a material, and causes sound waves to jump from one molecule to the next more quickly.

This explains why room-temperature air has a speed of sound of 346 m/s, while air at water’s freezing point (0°C / 32°F) has a speed of sound of 331 m/s.⁴ While this fascinating connection between thermal dynamics and acoustics is often overlooked, it can make a noteworthy difference in a room’s sound quality.

Speed of Sound Formula With Temperature

If you want to measure the average speed of sound for various temperatures, you can use this formula⁵:

v = 331 m/s + 0.61T

Here’s how the equation breaks down:

v is the speed of sound
331 m/s is the speed of sound at 0°C
0.61 is a constant that represents the increase in sound’s speed with every additional degree
T is the air’s temperature in Celcius

What is the Speed of Sound for Common Materials?

Now that you understand the basic components that affect the speed of sound, let’s take a look at how quickly sound moves through the following mediums²:

Gasses at 0°C or 32°F

Air – 331 m/s
Carbon dioxide – 259 m/s
Oxygen – 316 m/s
Helium – 965 m/s
Hydrogen – 1,290 m/s

Liquids at 20°C or 68°F

Ethanol – 1,160 m/s
Mercury – 1,450 m/s
Freshwater – 1,480 m/s
Sea water – 1,540 m/s

Solids

Rubber – 60 m/s
Polyethylene – 920 m/s
Lead – 1,210 m/s
Gold – 3,240 m/s
Marble – 3,810 m/s
Copper – 4,600 m/s
Aluminum – 5,120 m/s
Iron – 5,120 m/s
Glass – 5,640 m/s
Steel – 5,960 m/s
Diamond – 12,000 m/s

As you can see, the effect of these materials’ varying properties on the speed of sound is quite pronounced—sound travels nearly 35 times faster through a diamond than it does through air.⁶

Soundproofing Solutions

The speed of sound is a complex and fascinating phenomenon, but thankfully, soundproofing solutions tend to be relatively simple.

Here are some popular soundproofing solutions we offer at Acoustical Surfaces:

Sound Absorption Solutions

Soundproofing solutions have many valuable applications, but they’re not always right for your acoustical goals. Maybe you want to enhance the acoustics of a space instead, whether that involves dampening distracting echoes and reverberations or balancing the sound within a space. In this case, sound absorption is what you need.

While soundproofing materials isolate sound within a space, sound absorption materials are often soft and foamy, enabling them to soak up excess sound waves like a sponge and stop them from bouncing around, creating an unpleasant cacophony in their wake.

Some of our best-selling sound absorption products at Acoustical Surfaces are:

Learn More About Sound With Acoustical Surfaces

From music to meteorology, the speed of sound is an important concept. It’s especially relevant to understand how sound speeds change with varying levels of density, elasticity, and temperature.

By understanding the way sound travels through different materials, you can make smarter acoustical decisions. However, you don’t have to navigate this process alone—just reach out to our team of sound experts at Acoustical Surfaces. We’ve been providing comprehensive sound solutions for over 35 years.

If you want custom sound solutions for your space, whether that’s a classroom, restaurant, recording studio, or home, we can help you select the ideal products. Contact our team today to receive tailored soundproofing or sound absorption support.

Sources:

BYJU’s. Sound Waves. https://byjus.com/physics/sound-waves/
LibreTexts. 17.3: Speed of Sound. https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/17%3A_Sound/17.03%3A_Speed_of_Sound
SFU. Wavelength. https://www.sfu.ca/sonic-studio-webdav/handbook/Wavelength.html
Iowa State University. Sound. https://www.nde-ed.org/Physics/Sound/index.xhtml
University of Rhode Island. Sound Waves. https://penrose.uri.edu/labs/PHY275/sound_waves/sound_waves.pdf
Inspirit. Speed Of Sound Study Guide. https://www.inspiritvr.com/speed-of-sound-study-guide/