Wave speed on a string API

Computes the transverse wave speed v = sqrt(T/μ) on a stretched string from tension and linear mass density (or mass+length), with the fundamental frequency for a fixed-fixed length. Answers 'How fast does a wave travel on this string?', 'What is its fundamental pitch?'.

Price$0.04per request

MethodPOST

Route/v1/engineering/string-wave-speed

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

wavesstringwave-speedtensionlinear-densityfundamental-frequencyvibrationphysics

API URLhttps://x402.hexl.dev/v1/engineering/string-wave-speed

Integration docs

Example request

{
  "tensionN": 100,
  "linearDensityKgPerM": 0.01,
  "lengthM": 0.65
}

Example response

{
  "speedMps": 100,
  "linearDensityKgPerM": 0.01,
  "fundamentalFrequencyHz": 76.923077,
  "interpretation": "Wave travels at 100 m/s along the string."
}

Input schema

{
  "type": "object",
  "required": [
    "tensionN"
  ],
  "properties": {
    "tensionN": {
      "type": "number",
      "description": "String tension (N)",
      "examples": [
        100
      ]
    },
    "linearDensityKgPerM": {
      "type": "number",
      "description": "Linear mass density μ (kg/m)",
      "examples": [
        0.01
      ]
    },
    "massKg": {
      "type": "number",
      "description": "Total string mass (kg), with lengthM if μ not given",
      "examples": [
        0.0065
      ]
    },
    "lengthM": {
      "type": "number",
      "description": "String length (m), enables fundamental frequency",
      "examples": [
        0.65
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}