Oscillations and waves

Introduction to sound waves

Sound is a mechanical wave, usually longitudinal in gases and liquids; frequency determines pitch, while amplitude relates to intensity.

A vibrating tuning fork compresses and rarefies nearby air; pressure variations spread outward. The ear detects pressure oscillations, not air molecules traveling from source to ear.

Speed, wavelength, and intensity

In a given medium and condition, frequency is set by the source and wavelength obeys $lambda=v/f$. For an unabsorbed spherical wave, energy spreads over area proportional to $r^2$, so intensity falls approximately as $1/r^2$.

Quick check

Sound requires an elastic medium; in a vacuum no particles transmit oscillations, so sound cannot propagate. In gases, compressions and rarefactions travel along the wave direction, and sound speed rises as air temperature increases. Sound from a point source in a uniform medium spreads approximately spherically; its energy covers a larger area and intensity falls with distance.

When applying a model, state which quantities are held fixed and choose the appropriate reference frame. Keeping units beside numerical values helps prevent confusion between quantities or between measured and predicted values. After calculating, check dimensions, signs, and limiting cases: the result should fit the assumptions, such as small oscillations, a uniform medium, or negligible resistance. If real conditions differ, explain the discrepancy instead of applying a formula mechanically.

A useful physical check is to substitute special cases into the relation: equilibrium, maximum displacement, one full cycle, or no relative motion. These cases often make a quantity vanish or reach an extreme, exposing sign errors and confusion between period and frequency. When comparing experiments, change one condition at a time so that the cause of a changed result is clear.