Wave Speed Formula

The Formula

v = f\lambda (frequency times wavelength)

When to use: How fast the wave's shape moves forward through whatever it's traveling in.

Quick Example

A wave with frequency 5 Hz and wavelength 2 m has speed v = f\lambda = 5 \times 2 = 10 m/s.

Notation

v is the wave speed in m/s, f is the frequency in hertz (Hz), \lambda (lambda) is the wavelength in metres, and T is the period in seconds.

What This Formula Means

Wave speed is the distance a wave pattern travels each second through a medium.

How fast the wave's shape moves forward through whatever it's traveling in.

Formal View

For any periodic wave, the phase velocity is v = f\lambda = \lambda / T, where the speed depends solely on the properties of the medium (e.g., tension and density for a string, temperature for sound in air).

Worked Examples

Example 1

easy
A sound wave has a frequency of 440 \text{ Hz} and a wavelength of 0.773 \text{ m}. What is the speed of sound?

Solution

  1. 1
    Use the wave equation: v = f\lambda.
  2. 2
    Substitute the given values: v = 440 \times 0.773.
  3. 3
    v = 340.1 \text{ m/s}

Answer

v \approx 340 \text{ m/s}
The wave equation v = f\lambda applies to all types of waves. The speed of sound in air at room temperature is approximately 340 \text{ m/s}.

Example 2

medium
A seismic wave travels 60 \text{ km} in 10 \text{ s}. What is its speed? If the frequency is 2 \text{ Hz}, what is the wavelength?

Example 3

medium
A sound wave has frequency 440 Hz and wavelength 0.773 m. Calculate the speed of sound.

Common Mistakes

  • Confusing wave speed with the speed of the particles in the medium — wave speed is how fast the pattern moves, not how fast the medium oscillates.
  • Trying to change wave speed by changing frequency — in a given medium the speed is fixed; changing f changes \lambda instead.
  • Using inconsistent units: mixing cm for wavelength with m/s for speed without converting.

Common Mistakes Guide

If this formula feels simple in isolation but keeps breaking during real problems, review the most common errors before you practice again.

Wave Speed Mistakes

Why This Formula Matters

Wave speed explains why thunder arrives after lightning, why ultrasound can image the body, and why different materials transmit sound or vibrations at different rates. It also connects the three core wave quantities: speed, frequency, and wavelength.

Frequently Asked Questions

What is the Wave Speed formula?

Wave speed is the distance a wave pattern travels each second through a medium.

How do you use the Wave Speed formula?

How fast the wave's shape moves forward through whatever it's traveling in.

What do the symbols mean in the Wave Speed formula?

v is the wave speed in m/s, f is the frequency in hertz (Hz), \lambda (lambda) is the wavelength in metres, and T is the period in seconds.

Why is the Wave Speed formula important in Physics?

Wave speed explains why thunder arrives after lightning, why ultrasound can image the body, and why different materials transmit sound or vibrations at different rates. It also connects the three core wave quantities: speed, frequency, and wavelength.

What do students get wrong about Wave Speed?

Wave speed is fixed by the medium—changing frequency changes wavelength, not speed.

What should I learn before the Wave Speed formula?

Before studying the Wave Speed formula, you should understand: wavelength, frequency.

Want the Full Guide?

This formula is covered in depth in our complete guide:

Forces, Motion, and Energy: A Concept Bridge Guide →
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