Practice Derivation of the One-Dimensional Wave Equation - 17.2 | 17. Modelling – Vibrating String, Wave Equation | Mathematics (Civil Engineering -1)
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Derivation of the One-Dimensional Wave Equation

17.2 - Derivation of the One-Dimensional Wave Equation

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does transverse displacement refer to?

💡 Hint: Think about how strings move when plucked.

Question 2 Easy

Write the wave equation derived from the force analysis.

💡 Hint: Recall the relation between acceleration and displacement.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the equation for the wave speed (c)?

c = √(T/ρ)
c = T/√(ρ)
c = ρ/T

💡 Hint: Think about the properties of both tension and mass per unit length.

Question 2

The wave equation is a differential equation of which order?

True
False

💡 Hint: Consider the number of derivatives with respect to time and space.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider a string with mass density ρ = 0.01 kg/m and tension T = 10 N. Calculate the wave speed c and discuss its significance.

💡 Hint: Be sure to plug the values into the wave speed formula correctly.

Challenge 2 Hard

If the tension in the string is doubled while keeping the mass density constant, how does the wave speed change?

💡 Hint: Think about the relationship expressed in the wave speed formula.

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.