Sound Waves — Properties, Speed & Decibels

Sound waves are vibrations that move through matter such as air, water, or solids. If you need the quick picture, focus on three ideas: frequency, wavelength, and speed. They are related by

$$v = f\lambda$$

Here, $v$ is wave speed, $f$ is frequency, and $\lambda$ is wavelength. Decibels, written as dB, do not tell you how fast sound travels. They describe sound level on a logarithmic scale.

What Sound Waves Are

A sound wave needs a medium. It can travel through gases, liquids, and solids, but not through empty vacuum. The medium's particles do not move all the way from the source to your ear. They vibrate around equilibrium positions while the disturbance moves through them.

In air, a speaker cone moving outward creates a compression. Moving inward creates a lower-pressure region called a rarefaction. That repeating pressure pattern is what carries the sound.

Sound Wave Properties That Matter Most

Frequency. Frequency tells you how many oscillations happen each second. It is measured in hertz, where $1\ \mathrm{Hz} = 1\ \mathrm{s^{-1}}$. Higher frequency usually means higher pitch.

Wavelength. Wavelength is the distance between matching points on successive cycles, such as one compression to the next.

Amplitude. Amplitude is related to the size of the pressure variation or particle motion. A larger amplitude usually means a more intense sound.

Speed. Speed tells you how fast the disturbance moves through the medium. It is mainly controlled by the medium and its condition.

These ideas are connected. If the speed stays fixed and the frequency increases, the wavelength must decrease.

What Sets the Speed of Sound

The speed of sound is not a universal constant. It depends on the material and, in many cases, on conditions such as temperature.

In dry air at about $20^\circ\mathrm{C}$, the speed of sound is about

$$343\ \mathrm{m/s}$$

That value is only an approximation for that condition. In warmer air, sound travels faster. In liquids and many solids, sound typically travels faster than in air because the medium transmits compressions more effectively.

For many introductory problems, you are given the speed or told to use an approximate standard value. Once that value is set, $v = f\lambda$ is the main working relation.

Worked Example: Find the Wavelength of a Sound Wave

Suppose a tuning fork produces a tone of frequency $680\ \mathrm{Hz}$ in air at about $20^\circ\mathrm{C}$. Use $v = 343\ \mathrm{m/s}$ for the speed of sound. What is the wavelength?

Start from

$$\lambda = \frac{v}{f}$$

Substitute the values:

$$\lambda = \frac{343}{680}\ \mathrm{m}$$ $$\lambda \approx 0.504\ \mathrm{m}$$

So the wavelength is about $0.50\ \mathrm{m}$.

This example shows the main tradeoff clearly. In the same medium, speed stays fixed, so raising the frequency forces the wavelength to get shorter. If the frequency doubled, the wavelength would be cut in half.

What Decibels Mean in Sound

Decibels measure sound level on a logarithmic scale. For sound intensity level, a common definition is

$$\beta = 10 \log_{10}\left(\frac{I}{I_0}\right)$$

where $I$ is the intensity and $I_0$ is a reference intensity.

The key point is the logarithm. A change in decibels does not represent a linear change in intensity. If the sound intensity increases by a factor of $10$, the level increases by $10\ \mathrm{dB}$.

That is why decibel values can describe a very wide range of sound intensities without huge numbers. It is also why you should not treat dB values like ordinary linear measurements or use them to compare wave speed.

Common Mistakes with Sound Waves

Thinking sound can travel in vacuum

It cannot. Sound needs a material medium.

Assuming louder sounds move faster

In ordinary wave problems, louder means larger amplitude, not greater wave speed.

Mixing up frequency and speed

Frequency is set by the source. Speed is set by the medium and its condition. When sound enters a new medium, the frequency stays the same, while the wavelength usually changes.

Treating decibels as a linear scale

The dB scale is logarithmic. A small numerical change in dB can represent a large physical change in intensity.

Where Sound Waves Are Used

Sound wave ideas matter in music, room acoustics, ultrasound imaging, sonar, seismology, speaker design, and noise control. The same basic questions appear again and again: how fast does the wave travel, what sets its wavelength, how strong is it, and how does the medium change what you observe?

Try a Similar Problem

Try your own version by keeping the $680\ \mathrm{Hz}$ tone and changing the air temperature assumption, or by keeping the same speed and choosing a different frequency. That is a simple way to see when wavelength changes and when it does not.