Wave speed equals frequency multiplied by wavelength: v = fλ. Frequency is also the reciprocal of the period, f = 1 ÷ T.
This lesson is part of SPM Physics waves. Next, see how these quantities change in reflection, refraction and diffraction.
What do the wave quantities mean?
The wavelength λ is the distance between two neighbouring crests. The frequency f is how many complete waves pass a fixed point each second.
The period T is the time one wave takes to pass. The speed v is how far a crest travels each second.
Worked example: counting waves
An original ripple tank lets you count 12 complete waves passing a mark in 4.0 s. The distance between neighbouring crests is 5.0 cm.
Frequency = 12 ÷ 4.0 = 3.0 Hz. Period = 1 ÷ 3.0 = 0.33 s. The wavelength is 5.0 cm = 0.050 m, so the speed is v = fλ = 3.0 × 0.050 = 0.15 m s⁻¹.
Worked example: finding frequency from speed
A wave on a rope travels at 2.0 m s⁻¹ with a wavelength of 0.80 m. Rearrange the formula: f = v ÷ λ = 2.0 ÷ 0.80 = 2.5 Hz.
The period is T = 1 ÷ 2.5 = 0.40 s. Check by multiplying back: 2.5 × 0.80 = 2.0 m s⁻¹.
The mistake that costs marks
The common slip is to treat the number of waves counted as the frequency, without dividing by the time.
| Step | Wrong | Right |
|---|---|---|
| Frequency from 12 waves in 4.0 s | 12 Hz | 12 ÷ 4.0 = 3.0 Hz |
| Speed | 12 × 0.050 = 0.60 m s⁻¹ | 3.0 × 0.050 = 0.15 m s⁻¹ |
Frequency always means waves per second. If the time given is not one second, divide.
How do the numbers change for sound and radio?
The formula stays the same, but the numbers shift. Sound in air travels at about 340 m s⁻¹, and radio waves travel at 3.0 × 10⁸ m s⁻¹.
A note of frequency 170 Hz in air has wavelength 340 ÷ 170 = 2.0 m. A radio station broadcasting at 100 MHz = 1.00 × 10⁸ Hz has wavelength 3.0 × 10⁸ ÷ (1.00 × 10⁸) = 3.0 m.
Check yourself
A buzzer produces sound of frequency 680 Hz in air, where the speed of sound is 340 m s⁻¹. Find the wavelength and the period.
Answer
λ = v ÷ f = 340 ÷ 680 = 0.50 m.
T = 1 ÷ f = 1 ÷ 680 = 1.5 × 10⁻³ s.
Check: 680 × 0.50 = 340 m s⁻¹.
What to study next
The next lesson asks what happens to v, f and λ when a wave changes medium or meets an obstacle. Continue with explaining reflection, refraction and diffraction, then read waves from pictures in interpreting wave graphs.
For help with unit handling in wave calculations, see online one-to-one Physics tuition.