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 in which the particles of the medium oscillate parallel to the direction of wave propagation, creating alternating regions of compression (high pressure) and.

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).

Sense of Study hint: When identifying a longitudinal wave, check whether particles oscillate in the same direction the wave travels. Look for compressions (regions squeezed together) and rarefactions (regions spread apart). Sound in air is the most common example — air molecules vibrate back and forth along the direction the sound moves.

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

WavesSoundPressure Wave

Background Knowledge

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

waves