SPI Physics · Sound

Sound Waves and Their Speed

Sound is a longitudinal mechanical wave that needs a material medium, and it travels fastest in solids, slower in liquids and slowest in gases.

All Sound notes

Why this matters

Five questions in the bank, four EASY and one MODERATE: which wave needs a material medium, where sound is fastest, air against water, what affects the speed most, and what heat does to it. Every one is answered by the order solids, liquids, gases and the fact that warm air carries sound faster.

Concept 1 of 2: Sound as a mechanical wave: v = fλ

A vibrating object pushes the air next to it, that air pushes the next layer, and so on, so a pattern of squeezed and stretched air travels outwards. With no particles to push, as in a vacuum, there is no sound.

Definition

Sound is a mechanical wave: it needs a material medium (solid, liquid or gas) and cannot travel through a vacuum.
It is longitudinal: the particles move back and forth along the direction the wave travels, making compressions and rarefactions.
Speed $=$ frequency $\times$ wavelength, $v = f\lambda$ . Frequency is in hertz (Hz).
Humans hear about 20 Hz to 20 kHz. Below 20 Hz is infrasound; above 20 kHz is ultrasound.

Wave speed

v = f\lambda \qquad T = \frac{1}{f}

vspeed of the wave, in m/s
ffrequency, in hertz
λwavelength, in metres
Ttime period, in seconds

Worked example

A sound wave has a frequency of 500 Hz and a wavelength of 0.68 m. Find its speed.

Practice this conceptself-check · 4 quick reps

The same idea in a practice question:

Practice questionEasy

Example 1 · Sound · Sound Waves and Their Speed

Which of the following require material medium for propagation?

Thinking light needs a medium too

Light is an electromagnetic wave and crosses empty space from the Sun. Only mechanical waves, like sound, need a material medium.

Calling sound transverse

Sound in air is longitudinal: the air moves back and forth along the wave's path, making compressions and rarefactions.

Leaving kilohertz unconverted

Change kHz to Hz before using

v = f\lambda

. A 2 kHz note at 340 m/s has

\lambda = \frac{340}{2000} = 0.17

m, not 170 m.

Concept 2 of 2: How fast sound travels, and what changes it

Sound is passed from particle to particle. In a solid the particles are tightly bound, so the push passes on fastest; in a gas they are far apart, so it passes slowest. The medium matters far more than anything else.

Definition

Order of speed: solids > liquids > gases. In a vacuum sound does not travel at all.
The nature of the medium has by far the biggest effect.
In air, the speed rises with temperature, by about 0.6 m/s for each degree Celsius, and rises slightly with humidity.
The source, the loudness and the pitch do not change the speed in a given medium.

Medium	Speed of sound
Vacuum	Sound cannot travel
Air at 0 °C	about 331 m/s
Air at 20 °C	about 343 m/s
Water	about 1500 m/s, over four times the speed in air
Steel	about 5000 to 6000 m/s Fastest of the media the questions use.

Warmer air carries sound faster; colder air carries it slower.

Practice this conceptself-check · 4 quick reps

The same idea in a practice question:

Practice questionEasy

Example 2 · Sound · Sound Waves and Their Speed

The speed of sound is maximum in -

Sound is fastest in air

Air is the slowest of the three. Sound is fastest in solids such as steel, then liquids such as water, then gases.

The source sets the speed

Who or what makes the sound does not matter. In one medium at one temperature, every sound travels at the same speed.

Heat slows sound down

In air it is the reverse: the speed rises as the temperature rises.

Sound is slower in water than in air

Sound travels over four times as fast in water (about 1500 m/s) as in air (about 340 m/s), because a liquid's particles are closer together.

Drill 3 more on how fast sound travels, and what changes it

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Sound as a mechanical wave: v = fλ
Wave speed
$v = f\lambda \qquad T = \frac{1}{f}$

Reference tables (1)

How fast sound travels, and what changes it5 rows

Medium	Speed of sound
Vacuum	Sound cannot travel
Air at 0 °C	about 331 m/s
Air at 20 °C	about 343 m/s
Water	about 1500 m/s, over four times the speed in air
Steel	about 5000 to 6000 m/s Fastest of the media the questions use.

Warmer air carries sound faster; colder air carries it slower.

Watch out for (7)

Thinking light needs a medium too
→ Sound as a mechanical wave: v = fλ
Calling sound transverse
→ Sound as a mechanical wave: v = fλ
Leaving kilohertz unconverted
→ Sound as a mechanical wave: v = fλ
Sound is fastest in air
→ How fast sound travels, and what changes it
The source sets the speed
→ How fast sound travels, and what changes it
Heat slows sound down
→ How fast sound travels, and what changes it
Sound is slower in water than in air
→ How fast sound travels, and what changes it

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