What is the primary factor that determines the speed of sound in a medium?

The primary factor that determines the speed of sound in a medium is temperature. Sound travels as a mechanical wave, meaning it requires a medium (solid, liquid, or gas) to propagate. In general, the speed of sound increases with an increase in temperature within a specific medium. This occurs because higher temperatures provide more energy to the molecules in the medium, causing them to move more rapidly and thereby facilitating faster transmission of sound waves.

In gases, for instance, warmer air reduces the density, which allows sound waves to move more swiftly as the molecules collide more frequently. The relationship can be quantified in gases by the formula: ( v = \sqrt{\frac{\gamma RT}{M}} ), where ( v ) is the speed of sound, ( \gamma ) is the heat capacity ratio, ( R ) is the universal gas constant, ( T ) is the absolute temperature, and ( M ) is the molar mass of the gas.

While frequency, density, and wavelength also play roles in sound waves, they do not primarily determine sound speed. Frequency relates to pitch, wavelength is tied to the wave's characteristics, and density affects the propagation speed but is secondary to the influence of temperature.