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Waves · 12 min

Frequency and wavelength

Sound pitch relates to frequency, while wavelength helps explain how waves interact with spaces and obstacles.

01Why this matters

Sound pitch relates to frequency, while wavelength helps explain how waves interact with spaces and obstacles.

02See it

λ = 0.5 mA spatial trace: matching crests are one wavelength apart
The distance between adjacent matching crests is the wavelength. Sound particles oscillate along the direction of travel, not along this drawn curve.
v = 343 m/sf = 686 Hzλ = v/fλ = 0.5 m
Read left to right: v = 343 m/s → f = 686 Hz → λ = v/f → λ = 0.5 m. Each panel connects one part of the example.

03Understand it

Frequency counts cycles per second. Wavelength is the distance between matching points on adjacent wave cycles.

Wave speed equals frequency times wavelength: v = fλ. Frequency is measured in hertz, wavelength in metres and speed in metres per second. At fixed speed, higher frequency means shorter wavelength. Amplitude describes the size of a disturbance and is a separate property from frequency.

04Guided example

Find the wavelength of a 686 Hz sound wave travelling at 343 m/s.

  1. Use v = fλ and rearrange: λ = v/f.
  2. Substitute 343 m/s and 686 Hz: λ = 343/686.
  3. The wavelength is 0.5 m. The assumed sound speed is typical of air near room temperature.

05Try it

Wave speed 300 m/s, frequency 100 Hz. Wavelength?
A little hint

Divide speed by frequency.

06Practise it

Frequency 5 Hz, wavelength 2 m. Speed?
A little hint

Multiply frequency and wavelength.

Speed 20 m/s, wavelength 4 m. Frequency?
A little hint

Divide speed by wavelength.

07Use it in the real world

At 343 m/s, a 100 Hz tone has wavelength 3.43 m, while a 1,000 Hz tone has wavelength 0.343 m. These differences affect room acoustics.

Go a little deeper

The familiar sine-wave drawing is a plot of displacement or pressure variation. Sound in air is longitudinal; air particles oscillate back and forth rather than tracing the drawn transverse curve.

08Quick check

Sound speed 343 m/s, frequency 343 Hz. Wavelength?
A little hint

Use λ = v/f.

09Summary

Frequency counts cycles per second. Wavelength is the distance between matching points on adjacent wave cycles. The wavelength is 0.5 m. The assumed sound speed is typical of air near room temperature.

Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.

10Key idea

v = fλ

v: wave speed in m/s; f: frequency in Hz; λ (lambda): wavelength in m.

λ = v/f; f = v/λ for positive divisors

Find this in the formula library →