Speed of Sound Calculator with Solution

Speed of Sound Calculator with Solution

The speed of sound is a fascinating concept in physics that describes how quickly sound waves propagate through a medium. Here’s a comprehensive table summarizing all you need to know about the speed of sound:

AspectDetails
DefinitionThe speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium1.
Formulac=Ksρc=ρKs​​​, where KsKs​ is the isentropic bulk modulus and ρρ is the density1.
Speed in Air (20°C)Approximately 343 m/s or 767 mph36.
Factors Affecting Speed1. Density of the medium
2. Temperature of the medium
3. Elasticity of the medium25.
Effect of TemperatureSpeed increases with temperature. In air: v=331 m s+(0.6 m s C)×Tv=331 m s+(0.6 m s C)×T, where T is temperature in °C4.
Speed in Different MediaGenerally: Solids > Liquids > Gases2.
Equation for Airv=γRTMv=MγRT​​, where γγ is the adiabatic index, R is the gas constant, T is absolute temperature, and M is the molar mass7.
Simplified Air Equationv=20.05Tv=20.05T​, where T is absolute temperature in Kelvin7.
Wavelength Relationv=fλv=fλ, where f is frequency and λλ is wavelength6.

Key Points

  1. Medium Dependence: The speed of sound varies depending on the medium through which it travels. It’s generally fastest in solids, followed by liquids, and then gases2.
  2. Temperature Effect: In gases, the speed of sound increases with temperature. This is due to the increased kinetic energy of the particles at higher temperatures45.
  3. Density and Elasticity: While denser media generally slow down sound, more elastic media allow sound to travel faster. This explains why sound can travel faster in water than in air despite water being denser25.
  4. Measurement: The speed of sound can be measured using the equation: Speed = distance ÷ time. This is often done by timing how long it takes for an echo to return3.
  5. Practical Applications: Understanding the speed of sound is crucial in various fields, including acoustics, engineering, and meteorology. It’s used in sonar technology, architectural design, and even in weather forecasting.

By understanding these principles, you can grasp how sound behaves in different environments and why its speed can vary under different conditions.

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