Longitudinal Wave Examples in Physics

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

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 wave where the medium oscillates parallel to the direction of wave travel, forming compressions and rarefactions.

A slinky pushed back and forth: compressions and stretches travel along it.

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: The vibration direction is the same as the travel direction.

Common stuck point: Longitudinal waves can't be polarized (no perpendicular direction to filter).

Worked Examples

Example 1

easy
A longitudinal wave in a spring has compressions 0.4 \text{ m} apart. The wave frequency is 5 \text{ Hz}. What is the wave speed?

Solution

  1. 1
    The distance between consecutive compressions is the wavelength: \lambda = 0.4 \text{ m}.
  2. 2
    Wave speed: v = f\lambda = 5 \times 0.4 = 2 \text{ m/s}
  3. 3
    In a longitudinal wave, particles vibrate parallel to the wave's direction of travel.

Answer

v = 2 \text{ m/s}
In a longitudinal wave, particles oscillate back and forth along the same direction the wave travels. Compressions (high density) and rarefactions (low density) propagate through the medium.

Example 2

medium
Sound travels at 340 \text{ m/s} in air and 5100 \text{ m/s} in steel. A 1000 \text{ Hz} sound wave enters a steel rail. What is the wavelength in each medium?

Practice Problems

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

Example 1

medium
An ultrasound device emits sound at 2 \times 10^6 \text{ Hz} in human tissue (v = 1540 \text{ m/s}). What is the wavelength? Why is this frequency useful for medical imaging?

Example 2

hard
An earthquake produces both P-waves (v_P = 6000 \text{ m/s}, longitudinal) and S-waves (v_S = 3500 \text{ m/s}, transverse). A seismograph detects the P-wave 20 \text{ s} before the S-wave. How far away is the earthquake?
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Related Concepts

WavesSound

Background Knowledge

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

waves