Physics · Waves. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A progressive wave carries energy from one place to another, while the particles of the medium only vibrate about their mean positions. In a transverse wave the particles vibrate at right angles to the direction of travel (a wave on a string, light). In a longitudinal wave they vibrate along the direction of travel, forming compressions and rarefactions (sound in air).
Newton found the speed of sound by taking the changes in the air as isothermal. His answer, about 280 m s−1, was too low. Laplace said the compressions and rarefactions happen so quickly that no heat can flow, so they are adiabatic. This brings in the factor γ and gives a value close to the measured 332 m s−1.
Using Celsius temperature in v ∝ √T. Change to kelvin first: the speed doubles when the kelvin temperature becomes four times as large, not when the Celsius reading doubles.
Answer: Speed = 341 m s−1; wavelength = 0.68 m.
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