Sound Waves and Acoustics

Sound is a mechanical disturbance that travels through a medium. A vibrating source disturbs neighbouring particles, which pass the disturbance onward.

A guitar string, tuning fork and drum skin illustrate vibrating sources. In air, the vibrations create changing pressure regions.

Particles oscillate around their usual positions in the basic wave model. They do not travel from the source to the listener with the wave.

The wave transfers energy through the medium. This school-level description does not describe a bulk flow of air.

Air particles vibrate parallel to the direction of wave travel. That pattern makes ordinary sound in air a longitudinal wave.

• Compression: a region of increased pressure and density.
• Rarefaction: a region of decreased pressure and density.
• Wavelength: the distance between consecutive compressions or consecutive rarefactions.

A transverse wave has vibrations perpendicular to its direction of travel. Sound waves in solids can include transverse modes. Therefore, the longitudinal description needs its air-or-fluid context.

Can sound cross a vacuum? No. Mechanical sound needs a material medium to transmit the disturbance. Electromagnetic waves, including light, can travel through a vacuum.

Wave speed equals frequency multiplied by wavelength. For a repeating wave, the relationship is v = fλ.

• v: speed, measured in metres per second, or m/s.
• f: frequency, measured in hertz, or Hz.
• λ: wavelength, measured in metres, or m.

Frequency counts repetitions per second. Wavelength measures the spacing between matching points in the repeating pattern.

Worked example. A sound wave has speed 343 m/s and frequency 686 Hz.

λ = v/f = 343/686 = 0.50 m.

At the same speed, doubling frequency halves wavelength. Raising frequency alone does not make sound travel faster in the same ordinary medium.

Pitch is the perception of how high or low a sound is. Frequency is its main physical correlate.

A higher-frequency tone usually sounds higher in pitch. A lower-frequency tone usually sounds lower.

Amplitude describes the size of an oscillation. Increasing amplitude at the same frequency does not turn a low tone into a high tone.

Imagine playing one piano note softly and then strongly. The pitch can remain the same even though the sound becomes louder.

Intensity is a physical quantity; loudness is a human perception. Sound intensity measures energy flow per unit area per unit time.

Intensity is measured in watts per square metre, or W/m². Under fixed medium and frequency conditions, intensity increases with the square of wave amplitude.

For that comparison, doubling amplitude makes intensity four times as large. It does not automatically make perceived loudness four times as large.

A larger amplitude often makes a sound seem louder. However, the ear responds differently to different frequencies. Two sounds with equal intensity can therefore seem differently loud.

The familiar exam pairing is frequency–pitch and amplitude–loudness. That pairing does not prove that frequency has no effect on loudness perception.

Timbre is the sound quality that helps distinguish instruments. A violin and flute can differ in timbre despite similar pitch and loudness.

A regular musical tone may contain a fundamental frequency and several harmonics. Harmonics have frequencies that are whole-number multiples of the fundamental.

For a 200 Hz fundamental, the next two harmonics are 400 Hz and 600 Hz. Their relative strengths help shape the resulting waveform.

Not every sound contains a neat harmonic series. Instrument attacks, noise and other features also influence the sound quality.

A commonly quoted young-human hearing range is about 20 Hz to 20,000 Hz. Actual sensitivity varies between people and changes with age and hearing condition.

• Infrasonic: below about 20 Hz.
• Audible: within the approximate human hearing range.
• Ultrasonic: above about 20,000 Hz.

Ultrasound remains sound even though humans normally cannot hear it. Its frequency does not turn it into an electromagnetic wave.

Vocal folds in the larynx vibrate as air passes between them. The larynx is commonly called the voice box.

The mouth and other vocal-tract structures help shape the resulting sound into speech. Voice production therefore involves more than the vocal folds alone.

Hearing follows a different pathway. Sound makes the eardrum vibrate. Middle-ear bones transmit the vibrations towards the fluid-filled cochlea.

Sensory hair cells help convert the resulting movements into electrical signals. The auditory nerve carries signals towards the brain.

The eardrum does not interpret the sound by itself. Mechanical movement must be converted into signals that the nervous system can process.

Decibels express a logarithmic sound level relative to a reference. A sound-intensity level is not the same quantity as subjective loudness.

For intensity, β = 10 log₁₀(I/I₀) gives the level in decibels, or dB. Here, I is intensity and I₀ is the chosen reference intensity.

A tenfold intensity increase raises that level by 10 dB. The formula applies to intensity level; other decibel definitions use different underlying ratios.

Does 80 dB mark a universal pain threshold? No. A level of 80 dB should not be treated as a fixed threshold for physical pain. Hearing damage can occur without a painful sensation.

Risk depends on sound level and exposure duration. Noise pollution includes excessive or unwanted sound from traffic, machinery, loudspeakers and firecrackers.

The A-weighted decibel, or dBA, weights frequencies to approximate aspects of human hearing sensitivity. A bare dB figure needs its measurement context.

Sound speed depends on restoring stiffness and inertia together. Density supplies an inertia-related property, while the relevant elastic property supplies restoring force.

For a small disturbance in a fluid, v = √(B/ρ).

• B: bulk modulus, measured in pascals, or Pa.
• ρ: density, measured in kilograms per cubic metre, or kg/m³.
• v: sound speed, measured in m/s.

Bulk modulus measures resistance to compression. A large modulus means substantial pressure is needed for a given fractional volume change.

At fixed density, greater stiffness increases speed. At fixed stiffness, greater density reduces speed. Comparing two real materials requires considering both properties.

Typical comparisons. Sound travels at about 343 m/s in dry air at 20°C. In fresh water at 20°C, a useful approximate value is 1,480 m/s.

Steel’s speed depends on composition and wave type. A thin-rod model uses v = √(Y/ρ), where Y is Young’s modulus.

For illustrative values Y = 2.0 × 10¹¹ Pa and ρ = 8,000 kg/m³:

v = √(2.5 × 10⁷) = 5,000 m/s.

This is a model calculation, rather than a universal measured speed for steel. Bulk longitudinal waves in steel can have a different speed.

Sound often travels faster in familiar solids than liquids, and faster in liquids than gases. The ordering is not universal for every material or wave mode.

Air temperature affects sound speed. For a fixed-composition ideal gas, the basic model gives v = √(γRT/M).

• γ: ratio of heat capacities.
• R: universal gas constant, measured in J/(mol·K).
• T: absolute temperature, measured in kelvin.
• M: molar mass, measured in kg/mol.

With composition fixed and γ nearly constant, speed increases with the square root of absolute temperature. Celsius temperature cannot be inserted as T in this formula.

Humidity and composition can also affect the real value. “Room temperature” alone therefore does not specify every measurement condition.

An echo is a reflected sound heard as a separate repetition. Reverberation is persistence caused by overlapping reflections.

A distant hard surface can return a delayed sound. In a hall, many nearby surfaces produce overlapping reflections.

Sound-absorbing curtains and suitable acoustic panels can reduce reverberation. A rough surface may scatter sound without absorbing much energy. Roughness alone does not guarantee effective sound absorption.

How does echo timing reveal distance? For a stationary source and reflector, sound travels outward and back. With speed v and return time t, the distance is d = vt/2.

Suppose an underwater pulse returns after 0.10 s. Using v = 1,480 m/s, the distance is:

d = 1,480 × 0.10/2 = 74 m.

The division by two accounts for the return journey. The calculation assumes the stated speed and a simple reflected path.

Sound Navigation and Ranging (SONAR) uses sound to investigate underwater surroundings. Active sonar emits pulses and detects returning echoes.

Passive sonar listens for sounds without emitting its own probing pulse. Echo timing in active sonar can help determine distance.

Ordinary ultrasound imaging uses returning ultrasound echoes to show tissue structures. Differences in reflected signals help form the image.

Doppler ultrasound measures frequency changes associated with movement, such as blood flow. This is a particular ultrasound application.

The Doppler effect is a change in observed frequency from relative motion. An approaching sound source can be heard at a higher frequency. A receding source can be heard at a lower frequency.

Therefore, all sonography should not be explained solely as Doppler flow measurement.

Match the question’s physical situation with the relevant concept. A short exam pairing can simplify a relationship without describing every real-world condition.

The National Defence Academy and Naval Academy (NDA-NA) II 2016 General Ability Test (GAT) includes three baseline examples:

• Question 75: sound waves transfer energy through a medium in the basic wave model.
• Question 108: sound speed depends on elastic and inertia-related properties.
• Question 109: the standard pitch–frequency and loudness–amplitude distinction helps identify the intended statement.

Frequency still affects human loudness perception. The third example should not become a universal claim that frequency is irrelevant.

The Central Armed Police Forces (CAPF) Assistant Commandants (ACs)2025 Question 106 provides a sonography example. Doppler reasoning applies specifically to motion measurement. Ordinary ultrasound structure imaging also depends on reflected echoes.

The NDA-NA I 2025 echo example concerns reflection. The NDA-NA II 2025 example expands SONAR as Sound Navigation and Ranging.

NDA-NA II 2016 Q75 · Q108 · Q109 · CAPF ACs 2025 Q106 · Echo question · SONAR question