Acoustics: The Physics of Sound
Acoustics is the branch of physics that deals with the production, propagation, reception and perception of sound. Sound is a form of energy that travels through a material medium as a mechanical wave and produces the sensation of hearing in our ears. For students preparing for the APSC, Assam Direct Recruitment, SSC and other competitive examinations of Assam, acoustics is a high-yield topic because it connects simple everyday experiences, such as echoes in the hills of Assam, the tuning of the dhol and the pepa, and the working of sonar, with fundamental wave physics. A clear understanding of frequency, wavelength, speed, echo, reverberation, resonance and the Doppler effect allows you to answer both conceptual and numerical questions with confidence.
Basic Terms
- Vibration: A rapid to-and-fro motion of an object about its mean position; it is the source of all sound.
- Amplitude (A): The maximum displacement of a particle from its mean position. Its SI unit is the metre (m). It determines the loudness of sound.
- Frequency (f): The number of complete vibrations per second. Its SI unit is the hertz (Hz). It determines the pitch of sound.
- Time period (T): The time taken for one complete vibration, T = 1/f, measured in seconds.
- Wavelength (lambda): The distance between two consecutive compressions or rarefactions, measured in metres.
- Wave speed (v): The distance travelled by a wave per second, v = f lambda, measured in metre per second.
- Audible range: The range of frequencies that a normal human ear can hear, roughly 20 Hz to 20,000 Hz. Below 20 Hz is infrasound and above 20 kHz is ultrasound.
- Intensity and loudness: Intensity is the sound energy crossing unit area per second, measured in watt per square metre; loudness is related to it logarithmically and is measured in decibels (dB).
Core Concepts and Formulas
- Wave relation: v = f lambda and T = 1/f.
- Speed of sound in air: about 343 m/s at 20 degrees Celsius and about 332 m/s at 0 degrees Celsius; approximately v is nearly equal to 331 + 0.6 t metre per second, where t is the temperature in degrees Celsius.
- Newton's formula: v = square root of (E by rho); Laplace's correction: v = square root of (gamma P by rho), where gamma is the ratio of specific heats.
- Intensity of a point source: I = P by (4 pi r-squared), and I is proportional to A-squared f-squared.
- Loudness level: beta = 10 log of (I by I-zero) decibel, with I-zero = 10 to the power minus 12 watt per square metre.
- Echo condition: 2d = v t, so distance d = v t by 2; the minimum distance for a distinct echo is about 17.2 m at 20 degrees Celsius.
- Doppler effect for sound: f-prime = f (v plus or minus v-zero) by (v minus or plus v-s), where v-zero is the observer speed and v-s is the source speed.
- Fundamental frequency of a stretched string: f = (1 by 2L) square root of (T by mu), where mu is the mass per unit length.
- Frequency of a closed pipe: f = v by 4L; open pipe: f = v by 2L.
- Beats per second = absolute value of (f-one minus f-two).
- Sabine's formula for reverberation time: T = 0.16 V by A, with V in cubic metres and total absorption A in sabin.
Nature of Sound and How It Propagates
Sound is a mechanical, longitudinal wave. The particles of the medium vibrate to and fro along the direction of wave travel, forming alternating regions of compression, where the pressure is high, and rarefaction, where the pressure is low. Because sound needs a material medium, it cannot travel through a vacuum; this is why no sound is heard in outer space. Sound travels through solids, liquids and gases, but the particles do not move from the source to the listener; only the disturbance, that is the energy, is transferred. In a longitudinal wave, compressions and rarefactions replace the crests and troughs of a transverse wave. Sound can also be reflected, refracted, diffracted and absorbed, and it obeys the laws of reflection at a surface.
Speed of Sound in Different Media
The speed of sound depends on the elasticity and the density of the medium. In general, sound travels fastest in solids, more slowly in liquids and slowest in gases. For example, the speed of sound is about 5100 m/s in steel, about 1500 m/s in water and about 343 m/s in air at 20 degrees Celsius. In air, the speed increases with temperature because the molecules move faster; it is nearly independent of pressure at constant temperature, because pressure and density change together. Humidity slightly increases the speed of sound in air because water vapour is lighter than air. These values are frequently asked in objective examinations, and questions often compare the speed of sound in two media.
Reflection of Sound: Echo and Reverberation
When sound strikes a hard, large surface, it is reflected just like light. If the reflected sound reaches the listener after a delay of at least 0.1 second, it is heard as a distinct echo. Since the human ear cannot distinguish two sounds separated by less than 0.1 second, the minimum distance of a reflecting wall is about 17.2 m in air at 20 degrees Celsius. Echoes are used in sonar and in depth sounding. Reverberation is the persistence of sound in a hall due to repeated reflections; a small amount is pleasant, but excessive reverberation makes speech unclear. Sound-absorbing materials such as carpets, curtains and acoustic panels reduce reverberation, and Sabine's formula is used to design auditoriums.
Resonance, Natural Frequency and Musical Scales
Every object has a natural frequency at which it vibrates most readily. When a periodic force is applied at a frequency equal to the natural frequency, the amplitude of vibration becomes very large; this is resonance. A classic example is a glass breaking when a note of matching frequency is played loudly. Musical instruments exploit resonance: air columns in flutes and pipes, stretched strings in guitars and the ektara, and membranes in the dhol. The notes of a musical scale are related to frequency ratios, known as musical intervals. A stretched string produces a fundamental tone together with overtones, and the combination determines the quality, or timbre, of the sound.
Ultrasound and Infrasound and Their Applications
Sound waves above 20 kHz are called ultrasound, while those below 20 Hz are called infrasound. Ultrasound has a high frequency and can be focused into narrow beams, so it is used in medical sonography, in sonar for measuring sea depth and locating submarines, in cleaning delicate parts and in physiotherapy. Bats and dolphins use ultrasound for echolocation. Infrasound is produced by earthquakes, volcanoes and large machinery, and it can travel great distances; it is used to detect earthquakes and nuclear explosions.
The Doppler Effect
The Doppler effect is the apparent change in the frequency of sound due to the relative motion between the source and the observer. When the source and the observer approach each other, the observed frequency increases; when they move apart, it decreases. This explains the rise and fall of the pitch of a train whistle or the horn of a bus in Assam as it passes by. The observed frequency is given by f-prime = f (v plus or minus v-zero) by (v minus or plus v-s). The Doppler effect is used in police radar, in studying the motion of stars and in medical ultrasound to measure blood flow.
Applications of Acoustics
Acoustics has wide practical applications. It is used in the design of auditoriums, classrooms and concert halls where clarity of sound matters. It helps in noise control and pollution management in cities. Sonar and ultrasonography are major medical and defence tools. Musical instrument making, from the traditional Assamese pepa and xutuli to modern loudspeakers, depends on acoustical principles. Understanding acoustics also supports the study of communication systems and architecture.
Solving Numerical Problems
Most numerical questions on acoustics are solved by applying the wave equation and the Doppler formula. First list the known quantities with their units, then choose the correct relation. For an echo problem, remember that the sound travels to the reflector and back, so d = v t by 2. For beats, subtract the two frequencies. For Doppler problems, fix a sign convention: take the direction from the observer to the source as positive and substitute carefully. Always keep the units in SI, and check that the answer is physically reasonable; for example, a frequency cannot be negative.
Common Mistakes to Avoid
- Forgetting that sound cannot travel in a vacuum, and wrongly applying light-wave concepts to sound.
- Using the one-way distance instead of 2d in echo calculations.
- Mixing up the roles of amplitude and frequency: amplitude gives loudness, while frequency gives pitch.
- Using the wrong temperature value for the speed of sound when the question specifies it.
- Applying the Doppler formula with wrong signs for approaching and receding motion.
- Confusing the fundamental frequency of a closed pipe, v by 4L, with that of an open pipe, v by 2L.
- Treating reverberation as always undesirable, although a controlled amount is useful.
How to Prepare This Topic
- Read the definitions of the basic terms and memorise their SI units.
- Write down all the formulas on a single revision sheet and understand when each one applies.
- Practise at least twenty numerical problems on echo, beats, strings, pipes and the Doppler effect.
- Relate each concept to a real-life example that you can observe, such as echoes in the hills or the tuning of a dhol.
- Solve previous-year question papers and take timed mock tests to improve speed and accuracy.
Frequently Asked Questions
Why can sound not travel through a vacuum?
Sound is a mechanical wave and needs the particles of a medium to vibrate and carry energy. In a vacuum there are no particles, so sound cannot propagate.
What is the difference between an echo and reverberation?
An echo is a single distinct reflected sound heard after at least 0.1 second, while reverberation is the persistence of many overlapping reflections that makes sound continue in a hall.
What is the audible range of the human ear?
Approximately 20 Hz to 20,000 Hz. Frequencies below 20 Hz are infrasound and frequencies above 20 kHz are ultrasound.
What is the Doppler effect?
It is the apparent change in the frequency of a wave due to relative motion between the source and the observer. The frequency increases when they approach and decreases when they move apart.
How is the speed of sound related to temperature?
In air the speed increases with temperature, approximately as v is nearly equal to 331 + 0.6 t metre per second, because warmer air molecules have greater average kinetic energy.