How Do You Calculate Wave Speed (v = fλ)?

Calculate wave speed by multiplying the wave's frequency by its wavelength:

$$v=f\lambda$$

Use frequency in hertz and wavelength in metres to obtain wave speed in metres per second. This relationship is part of IB Physics C.2 Wave model and applies at both SL and HL.

The Reasoning

During one time period, a travelling wave moves forward by one wavelength. Frequency is the number of complete oscillations produced per second, so multiplying distance per oscillation by oscillations per second gives distance travelled per second.

Equivalently, the period is $T=1/f$. Since the wave travels one wavelength in one period, $v=\lambda/T$. Substituting $T=1/f$ gives $v=f\lambda$.

Always convert prefixes first. For example, $25\,\text{cm}=0.25\,\text{m}$ and $4.0\,\text{kHz}=4.0\times10^3\,\text{Hz}$.

For a wave with $f=50\,\text{Hz}$ and $\lambda=0.80\,\text{m}$:

$$v=(50)(0.80)=40\,\text{m s}^{-1}$$

A prefix-based example shows why conversions matter. If $f=2.5\,\text{kHz}$ and $\lambda=12\,\text{cm}$, convert them to $2.5\times10^3\,\text{Hz}$ and . Therefore,

$$v=(2.5\times10^3)(0.12)=3.0\times10^2\,\text{m s}^{-1}$$

Choose the form that isolates the required quantity:

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

For sound travelling at $340\,\text{m s}^{-1}$ with $f=680\,\text{Hz}$, $\lambda=340/680=0.50\,\text{m}$.

Use the equation with any travelling wave, including sound, water waves, and electromagnetic waves. However, do not assume every wave has the same speed. The medium and its physical properties determine the speed of a mechanical wave, while electromagnetic waves travel at $c$ only in vacuum. When a wave crosses a boundary, its frequency remains unchanged, but its speed and wavelength may change.

A common misconception is that increasing frequency automatically increases wave speed. In a fixed, non-dispersive medium, speed is determined by the medium, so increasing frequency decreases wavelength proportionally. For electromagnetic waves in a vacuum, use $c=3.00\times10^8\,\text{m s}^{-1}$. The equation describes the propagation speed of the wave, not the oscillation speed of particles in a mechanical wave.

IB Exam Technique

For a Calculate question, show the equation, substitution, and final value. Check that $\text{Hz}\times\text{m}=\text{m s}^{-1}$, convert all prefixes before substituting, and distinguish wave speed from particle motion.