Acoustic Phenomena

SYLLABUS

Sound waves: Pressure amplitude, Characteristics of sound: Intensity; loudness, quality and pitch, Doppler’s effect.

What is This Chapter About?

Close your eyes and listen. The world reaches you entirely through sound — voices, music, traffic, birdsong, rain. All of these are acoustic phenomena: the production, propagation, and perception of sound waves. But sound is more than just something we hear. It is a precisely quantifiable physical phenomenon with measurable properties that determine whether a sound is loud or soft, high-pitched or low, pleasant or harsh.

Chapter 9 of NEB Grade 12 Physics explores the science of sound in depth. It characterises sound waves quantitatively, examines the subjective qualities of sound that we perceive, and introduces the Doppler effect — one of the most important and widely applied phenomena in all of wave physics. Carrying 5 teaching hours, this chapter connects wave physics directly to music, medicine, astronomy, and everyday technology.

Key Concepts You Will Learn

Sound Waves as Pressure Waves

Sound is a longitudinal mechanical wave — the particles of the medium oscillate parallel to the direction of wave propagation, creating alternating regions of compression (high pressure) and rarefaction (low pressure). These pressure variations travel through the medium as a sound wave.

The pressure amplitude ([latex]\Delta P_{max}[/latex]) of a sound wave is the maximum variation in pressure from the equilibrium value. It is related to the displacement amplitude (A) of the medium particles by: [latex]\Delta P_{max} = B k A[/latex], where B is the bulk modulus of the medium and k is the wave number. This relationship shows that sound can be described either as a displacement wave or as a pressure wave — two equivalent but complementary descriptions.

Characteristics of Sound

Sound has four perceptible characteristics, each corresponding to a measurable physical quantity:

Intensity is the power carried by a sound wave per unit area perpendicular to the direction of propagation: [latex]I = \frac{P}{A}[/latex], measured in W/m². Intensity is an objective, physically measurable quantity.

Loudness is the subjective perception of intensity by the human ear. Because the ear responds logarithmically to intensity, loudness is measured in decibels (dB): [latex]L = 10\log_{10}\frac{I}{I_0}[/latex], where [latex]I_0 = 10^{-12}[/latex] W/m² is the threshold of hearing. A sound 10 times more intense sounds about twice as loud — the logarithmic scale captures this perceptual compression.

Pitch corresponds to the frequency of the sound wave. High-frequency vibrations produce high-pitched sounds (like a whistle); low-frequency vibrations produce low-pitched sounds (like a bass drum). The human ear can detect frequencies roughly between 20 Hz and 20,000 Hz.

Quality (or timbre) distinguishes sounds of the same pitch and loudness produced by different instruments. A piano and a violin playing the same note at the same volume sound different because they produce different combinations of harmonics (overtones) along with the fundamental frequency. Quality depends on the waveform — the shape of the sound wave — which in turn depends on which harmonics are present and in what proportions.

Doppler Effect

The Doppler effect is the change in the observed frequency of a wave when there is relative motion between the source and the observer. It is one of the most important and far-reaching results in wave physics.

When a source of sound moves toward a stationary observer, the sound waves are compressed in front of the source — the wavelength decreases and the observed frequency increases. The observer hears a higher pitch than the source actually produces. Conversely, when the source moves away, the waves are stretched — wavelength increases, frequency decreases, and the observer hears a lower pitch. This is the familiar experience of a siren sounding higher as an ambulance approaches and lower as it passes and recedes.

The general Doppler formula for sound is:

[latex]f’ = f\left(\frac{v \pm v_o}{v \mp v_s}\right)[/latex]

where [latex]f'[/latex] is the observed frequency, f is the source frequency, v is the speed of sound, [latex]v_o[/latex] is the speed of the observer, and [latex]v_s[/latex] is the speed of the source. The upper signs apply when the source and observer move toward each other (increasing frequency), and the lower signs apply when they move apart (decreasing frequency).

Applications of the Doppler Effect

The Doppler effect has extraordinarily wide applications across science and technology. In medicine, Doppler ultrasound measures the speed of blood flow through arteries and veins — the shift in reflected ultrasound frequency reveals the velocity of red blood cells, allowing doctors to detect blockages and clots. In astronomy, the Doppler shift of light from distant galaxies reveals that they are receding from us — the foundation of our understanding of the expanding universe. In radar and speed guns, the frequency shift of reflected radio waves or sound waves reveals the speed of vehicles, aircraft, and weather systems. In sonar, the Doppler shift helps submarines detect the motion of other underwater objects.

Why This Chapter Matters for NEB Exams

Acoustic Phenomena is examined consistently and thoroughly in NEB Grade 12 Physics. The Doppler effect formula — applying it to various combinations of moving sources and observers — generates numerical problems that appear in virtually every board paper. Characteristics of sound (intensity, loudness, pitch, quality) are standard short-answer questions, and the distinction between intensity (objective) and loudness (subjective) is a frequent conceptual question. The decibel scale and its logarithmic nature are also examined. Applications of the Doppler effect in medicine and astronomy are popular questions requiring students to connect physics to real-world contexts.

Important Topics to Focus On

• Sound as a longitudinal pressure wave — displacement amplitude and pressure amplitude
• Four characteristics of sound: intensity, loudness, pitch, and quality
• Intensity in W/m² and the decibel scale: [latex]L = 10\log_{10}\frac{I}{I_0}[/latex]
• Distinction between intensity (physical) and loudness (perceptual)
• Pitch and frequency — audible range of human hearing
• Quality (timbre) and its relationship to harmonics
• Doppler effect — physical explanation for moving source and moving observer
• Doppler formula: [latex]f’ = f\left(\frac{v \pm v_o}{v \mp v_s}\right)[/latex]
• All four cases: source moving toward/away from observer, observer moving toward/away from source
• Combined motion of source and observer
• Applications of Doppler effect in medicine, astronomy, radar, and sonar
• Numerical problems on Doppler effect under various conditions

Connection to Other Chapters

Acoustic Phenomena builds directly on Chapter 7 (Mechanical Waves) — the speed of sound v in the Doppler formula comes from that chapter — and Chapter 8 (Waves in Pipes and Strings) — the harmonics and overtones that determine sound quality are standing waves in pipes and strings. The concept of intensity connects to Chapter 12 of Grade 11 (Rate of Heat Flow) through radiation intensity, and the logarithmic decibel scale connects to mathematical concepts used throughout physics. The Doppler effect for light — which follows a different, relativistic formula — connects conceptually to Chapter 25 (Recent Trends in Physics) where gravitational waves and the expanding universe are discussed.