What is linear mass density (μ)?

Linear mass density is the mass per unit length of the string, measured in kg/m. For example, a 2 m string with mass 0.02 kg has μ = 0.01 kg/m.

What does the formula v = sqrt(T/μ) mean?

It means wave speed equals the square root of tension (in Newtons) divided by linear mass density (in kg/m). Higher tension or lower density increases the wave speed.

How does frequency relate to wave speed?

Wave speed v = f × λ, where f is frequency in Hz and λ (lambda) is wavelength in meters. This formula applies to any wave, not just strings.

What units does this calculator use?

Tension in Newtons (N), linear mass density in kg/m, frequency in Hz, wavelength in meters, and wave speed in m/s.

What is a sample calculation?

A string with T = 100 N and μ = 0.01 kg/m gives v = sqrt(100 / 0.01) = sqrt(10000) = 100 m/s.

Does this work for longitudinal waves?

No. The v = sqrt(T/μ) formula is specific to transverse waves on a stretched string. Longitudinal waves in solids use v = sqrt(E/ρ) where E is the elastic modulus.

Wave Speed On String Calculator

Name: Wave Speed On String Calculator
Availability: InStock
Author: Nham Vu

Calculate transverse wave speed on a string from tension and linear mass density, or from frequency and wavelength.

Inputs

Tension (T)

Linear mass density (μ)

kg/m

Formula: v = √(T / μ)

Result

Enter values and click Calculate

Quick Reference

Tension / Density

v = √(T / μ)

T in N, μ in kg/m

Frequency / Wavelength

v = f × λ

f in Hz, λ in m

Summary

Calculate transverse wave speed on a string from tension and linear mass density, or from frequency and wavelength.

How it works

Select the formula you want to use: Tension/Density or Frequency/Wavelength.
Enter the known values in the input fields.
Click Calculate to get the wave speed instantly.
Use the swap button to quickly switch between formulas.
Results are rounded to 4 significant figures for clarity.

Use cases

Physics homework and exam problems involving wave mechanics.
Engineering analysis of vibrating strings, cables, and wires.
Musical acoustics — relating string tension to wave speed.
Lab work verifying v = sqrt(T/μ) with measured tension and density.
Converting between frequency-wavelength and tension-density representations.
Checking units consistency in wave-speed derivations.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu