Sound

A. Production of Sound:

Sound is produced by mechanical vibrations of material bodies. When a body vibrates, it transfers kinetic energy to adjacent molecules in the surrounding medium.

• Human Voice: Air expelled from lungs causes the two vocal cords in the larynx (voice box) to vibrate.
• Musical Instruments: Vibrating strings (guitar, sitar), vibrating membranes (tabla, drums), vibrating air columns (flute, trumpet).

B. Sound Requires a Material Medium (The Bell-Jar Experiment):

1. An electric bell is suspended inside an airtight glass bell jar connected to a vacuum suction pump.
2. When the electric circuit is closed, the bell hammer strikes the gong, and the ringing sound is clearly heard.
3. As the vacuum pump gradually extracts the air from inside the jar, the sound grows progressively fainter.
4. When a near-total vacuum is created, the hammer can still be seen striking the gong vigorously, but NO sound is heard at all!
5. Conclusion: Sound is a mechanical wave that cannot travel through a vacuum. It strictly requires a material medium (solid, liquid, or gas).

A. Definitions:

• Compressions ($C$): Regions of high pressure and high molecular density.
• Rarefactions ($R$): Regions of low pressure and low molecular density.
• Amplitude ($A$): The maximum displacement of a vibrating particle from its central mean position (Unit: meter, $\text{m}$).
• Time Period ($T$): The time taken to complete one full oscillation (Unit: second, $\text{s}$).
• Frequency ($f$ or $\nu$): The number of complete vibrations per second (SI Unit: Hertz, $\text{Hz}$): $$f = \frac{1}{T}$$
• Wavelength ($\lambda$): The physical distance between two successive compressions or rarefactions (Unit: meter, $\text{m}$).

B. The Wave Equation:

A. Medium Elasticity & Density:

Sound travels fastest through solids (most elastic and densely packed atoms), slower through liquids, and slowest through gases:

• Speed in Steel $\approx 5,000\text{ m/s}$.
• Speed in Water $\approx 1,500\text{ m/s}$.
• Speed in Air ($20^\circ\text{C}$) $\approx 340\text{ m/s}$.

B. Thunder vs Lightning:

In a thunderstorm, electrical discharge produces lightning and thunder simultaneously at the exact same instant. However:

• Light travels at an immense speed of $c = 300,000,000\text{ m/s}$ ($3 \times 10^8\text{ m/s}$), reaching our eyes almost instantaneously ($t \approx 0$).
• Sound travels at a modest speed of only $\approx 340\text{ m/s}$, taking several seconds to traverse each kilometer of air.
• Hence, the flash of lightning is seen first, followed by the roar of thunder several seconds later.

A. Three Characteristics of Sound:

1. Pitch (Shrillness): Determined strictly by Frequency ($f$). Higher frequency produces a sharper, shriller pitch (e.g., female voice, whistle, mosquito buzzing); lower frequency produces a grave, flat pitch (e.g., male voice, lion roar).
2. Loudness: Determined by the square of Amplitude ($A^2$). Greater amplitude transmits more vibrational energy to the ear.
3. Quality (Timbre): Distinguishes sounds of the same pitch and loudness produced by different instruments (e.g., flute vs violin), governed by the shape of the sound wave and presence of overtones/harmonics.

B. Frequency Spectrum:

• Infrasonic Sound ($< 20\text{ Hz}$): Below human hearing; emitted by earthquakes, volcanoes, elephants, and whales.
• Audible Sound ($20\text{ Hz} - 20,000\text{ Hz}$): The human sonic spectrum.
• Ultrasonic Sound ($> 20,000\text{ Hz}$ or $20\text{ kHz}$): Above human hearing; utilized by bats for echolocation, dolphins, SONAR (Sound Navigation and Ranging), and medical ultrasonography.