Key Points

Sound is a form of energy that is produced by vibrating objects. A vibration is a rapid back-and-forth motion of an object about a central position.

Sound waves are mechanical waves, which means they require a medium (solid, liquid, or gas) to travel. They are also longitudinal waves, where the particles of the medium oscillate parallel to the direction of wave propagation.

Sound propagates as a series of compressions and rarefactions. A compression (C) is a region of high pressure and density, while a rarefaction (R) is a region of low pressure and density.

Wavelength is the distance between two consecutive compressions (C) or two consecutive rarefactions (R). It is represented by the Greek letter lambda ($\lambda$) and its SI unit is the meter (m).

Frequency is the number of complete oscillations per unit time. It is represented by the symbol nu ($\nu$) and its SI unit is Hertz (Hz).

The time period ($T$) is the time taken for one complete oscillation. It is the reciprocal of the frequency, given by the formula $T = \frac{1}{\nu}$. The SI unit for time period is the second (s).

Amplitude (A) is the maximum displacement or disturbance of the medium's particles from their mean position. The loudness of a sound is primarily determined by its amplitude; a larger amplitude results in a louder sound.

Pitch is the characteristic of a sound that allows us to distinguish a sharp sound from a flat one. It is determined by the frequency of the sound wave; a higher frequency corresponds to a higher pitch.

The speed of a sound wave ($v$) is related to its wavelength ($\lambda$) and frequency ($\nu$) by the fundamental equation $v = \lambda \nu$. This means speed is the product of wavelength and frequency.

The speed of sound depends on the properties of the medium through which it travels. In general, the speed of sound is fastest in solids, slower in liquids, and slowest in gases ($v_{\text{solid}} > v_{\text{liquid}} > v_{\text{gas}}$).

Sound waves bounce off a surface in the same way that light does, following the laws of reflection. The angle of incidence is equal to the angle of reflection, and both lie in the same plane as the normal.

An echo is a sound heard after reflection from a distant object like a cliff or a wall. To hear a distinct echo, the time interval between the original sound and the reflected sound must be at least $0.1$ seconds.

The minimum distance ($d$) to a reflecting surface for hearing a distinct echo is calculated by $d = \frac{v \times t}{2}$. Taking the speed of sound $v$ as $344 \text{ m/s}$ and time $t$ as $0.1 \text{ s}$, the minimum distance is approximately $17.2$ m.

The range of frequencies that an average human can hear is from about $20$ Hz to $20,000$ Hz (or $20$ kHz). Sounds outside this range are inaudible to humans.

Sounds with frequencies below the audible range of $20$ Hz are called infrasound. Sounds with frequencies above the audible range of $20$ kHz are called ultrasound.