Waves Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Waves.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

A disturbance that transfers energy and information through space or a medium without permanently displacing the matter it travels through.

Energy traveling through something—like ripples on water. The water stays put; the ripple moves.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Waves transfer energy and information through a medium without transporting matter itself.

Common stuck point: The medium (water, air) oscillates in place; only the pattern moves forward.

Sense of Study hint: When solving a wave problem, first identify the type of wave (transverse or longitudinal) and the medium. Then note the key properties: wavelength, frequency, amplitude, and speed. Use v = f\lambda to relate speed, frequency, and wavelength. Remember that the medium oscillates but does not travel with the wave.

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Wave Speed Mistakes

Worked Examples

Example 1

easy
A wave has a frequency of 5 \text{ Hz} and a wavelength of 2 \text{ m}. What is the wave speed? How far does the wave travel in 10 \text{ s}?

Solution

  1. 1
    Use the wave equation: v = f\lambda = 5 \times 2 = 10 \text{ m/s}.
  2. 2
    Distance traveled in 10 \text{ s}: d = vt = 10 \times 10 = 100 \text{ m}
  3. 3
    In 10 \text{ s}, 50 complete waves pass any fixed point (5 per second for 10 seconds).

Answer

v = 10 \text{ m/s}, \quad d = 100 \text{ m}
A wave is a disturbance that transfers energy without transferring matter. The wave equation v = f\lambda relates the three fundamental wave properties: speed, frequency, and wavelength.

Example 2

medium
A wave pulse travels along a rope at 4 \text{ m/s}. The rope is 12 \text{ m} long with one end fixed. How long does it take for the pulse to travel to the fixed end and return?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
Water waves in a ripple tank have a wavelength of 0.03 \text{ m} and travel at 0.12 \text{ m/s}. What is the frequency? How many complete waves pass a point in 15 \text{ s}?

Example 2

hard
A wave on a string has the equation y(x,t) = 0.05 \sin(4\pi x - 8\pi t) (SI units). What are the amplitude, wavelength, frequency, and wave speed?
← Back to Waves Common Mistakes Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

energysimple harmonic motion