Sound and Waves

Understand what a wave is, how sound travels, and the key properties of waves — frequency, wavelength, amplitude, and speed.

What is a Wave?

A wave is a disturbance that transfers energy through a medium (or through space) without permanently displacing matter.

Wave type	Vibration direction vs travel	Example
Transverse	Perpendicular	Light, water ripples
Longitudinal	Parallel (compressions)	Sound

Key Wave Properties

Wave Speed

v = f \cdot \lambda

v = speed (m/s), f = frequency (Hz = cycles per second), λ = wavelength (m).

Amplitude (A) — maximum displacement from the rest position; related to the energy of the wave.
Frequency (f) — how many complete waves pass a point per second.
Wavelength (λ) — distance from one crest (or compression) to the next.
Period (T) — time for one complete wave: $T = \dfrac{1}{f}$ .

Sound

Sound is a longitudinal mechanical wave — it needs a medium (solid, liquid, or gas) to travel. It cannot travel through a vacuum.

Speed of sound in different media:

Medium	Speed
Air (20 °C)	≈ 343 m/s
Water	≈ 1 480 m/s
Steel	≈ 5 000 m/s

Sound travels faster in denser/stiffer materials.

Pitch and Loudness

Pitch — perceived frequency. High frequency → high pitch.
Loudness — perceived amplitude. Large amplitude → loud sound.

Human hearing range: approximately 20 Hz – 20 000 Hz.

Infrasound < 20 Hz (elephants, earthquakes)
Ultrasound > 20 000 Hz (bats, medical imaging)

Note The Doppler effect: a source moving toward you sounds higher pitched; moving away sounds lower pitched.

1
Write down v = fλ
Identify which two values are known.
2
Rearrange
f = v/λ or λ = v/f.
3
Substitute and calculate
Keep units consistent (m, Hz, m/s).

A sound wave in air has a frequency of 440 Hz. Find its wavelength. (v = 343 m/s)

$\lambda = \frac{v}{f} = \frac{343}{440} \approx 0.78 \text{ m}$

Real world: musical instruments and pitch

A guitar string vibrating at 440 Hz produces the note A4. Halving the string length doubles the frequency to 880 Hz (A5, one octave higher). The wavelength of this 440 Hz sound in air: $\lambda = \frac{343}{440} \approx 0.78\text{ m}$ . Instrument design is entirely based on controlling frequency and wavelength.

Real world: ultrasound medical scanning

A medical ultrasound scanner emits pulses at about 3–10 MHz (millions of Hz), far above the 20 000 Hz human hearing limit. The pulses reflect off internal organs and return to the probe. Because $v = f\lambda$ , the short wavelengths at high frequency give fine detail (small structures can be resolved). Ultrasound is used to image babies in the womb and detect kidney stones.

Real world: noise-cancelling headphones

Active noise-cancelling headphones use a microphone to detect incoming sound waves, then produce an equal and opposite pressure wave to cancel them. This works on the principle of destructive interference. The Doppler shift principle is also used in speed radar guns — the reflected frequency differs from the emitted frequency depending on the vehicle's speed.

Tip Remember

v = f\lambda

: speed = frequency × wavelength. If frequency increases, wavelength decreases (speed stays constant in the same medium). This is why high-pitched sounds have short wavelengths.

Practice Problems

A wave has frequency 200 Hz and wavelength 1.5 m. What is its speed?

Show answer

v = 200 × 1.5 = 300 m/s.

Can sound travel in outer space? Why?

Show answer

No — sound is a mechanical wave and needs a material medium. Space is a vacuum.

A bat emits ultrasound at 50 000 Hz. What is the wavelength in air? (v = 343 m/s)

Show answer

λ = 343 / 50 000 = 0.00686 m ≈ 6.9 mm.