NDA Physics · Formula sheet

Sound formulas

4 formulas, 6 reference tables and 25 common traps for NDA Physics Sound, grouped by subtopic.

Foundations: What Sound Is and How We Hear It

The human ear — anatomy chain that converts pressure to nerve impulses

Part	Function / mechanism	Note
Pinna (outer ear)	Funnels sound into the ear canal	Acoustic collector — no signal conversion
Eardrum (tympanic membrane)	Sound waves $\to$ mechanical vibration	Thin membrane at the end of the ear canal
Ossicles (malleus, incus, stapes)	Mechanical amplification & impedance matching	Three tiny bones in the middle ear
Cochlea	Mechanical pressure $\to$ electrical (nerve impulses)	Fluid-filled spiral in the inner ear — the biological mic NDA 2022 Sep — the pressure $\to$ electrical converter IS the cochlea (not the eardrum, ossicles, or auditory nerve).
Auditory nerve	Carries nerve signals from cochlea to brain	Transmission, not conversion

Each stage performs a distinct physical conversion. Distractors swap the cochlea (the converter) with the eardrum (mechanical-only) or the auditory nerve (transmission-only).

Common traps

Sound is longitudinal — and that's exactly why it CANNOT polarize

Polarization is a phenomenon of TRANSVERSE waves only — it restricts the plane of oscillation perpendicular to wave direction. Sound oscillates ALONG the wave direction, so there is no perpendicular plane to polarize. (The full "what sound can/can't do" trap-row table is in Subtopic 3.)

Sound vs light — both waves, but VERY different

Sound = mechanical + longitudinal + needs medium + speed

\approx 340

m/s in air. Light = electromagnetic + transverse + travels in vacuum + speed

\approx 3 \times 10^8

m/s. An option offering "sound is electromagnetic" or "sound is transverse" is always wrong.

Amplitude is measured in pressure (Pa), NOT decibels

Amplitude of a sound wave is the maximum displacement of particles (metres) or, more often for sound, the maximum pressure variation (Pascals). Decibels (dB) measure intensity LEVEL — a logarithmic ratio relative to a reference intensity. dB is NOT a unit of amplitude. NDA 2022 Sep tested exactly this distinction.

Loudness depends on amplitude, NOT frequency

A common distractor: "loudness depends on frequency" or "loudness depends on velocity". Both wrong. Frequency drives PITCH; loudness is driven by amplitude. The ear's response curve does have a mild frequency dependence, but for NDA purposes: amplitude only.

Cochlea, not eardrum, is the mechanical $\to$ electrical converter

The EARDRUM converts sound to MECHANICAL vibration (acoustic to mechanical). The OSSICLES amplify mechanical vibration mechanically. The COCHLEA is where mechanical pressure finally becomes ELECTRICAL nerve impulses. Three distinct stages — distractors often swap them.

How We Measure Sound — v = fλ, Speed, and the Frequency Bands

Learn this subtopic in the notes

Frequency, period, wavelength — and v = fλ

Wave equation

v = f\lambda

$v$ wave speed (m/s)
$f$ frequency (Hz)
$\lambda$ wavelength (m)

Speed of sound depends on the MEDIUM — not on f, not on P (at constant T)

Speed of sound in an ideal gas

v = \sqrt{\dfrac{\gamma P}{\rho}} = \sqrt{\dfrac{\gamma R T}{M}}

$\gamma$ adiabatic index ( $C_p/C_v$ )
$P$ pressure (Pa)
$\rho$ density (kg/m^3)
$T$ absolute temperature (K)
$M$ molar mass (kg/mol)

Bands and scales — audible / infra / ultrasonic, Mach, sound speeds, decibel, Richter

What	Value / range	Note
Audible frequency range (human ear)	20 Hz to 20 000 Hz	Drilled most years — memorise both endpoints
Infrasonic	< 20 Hz	Below the lower limit of human hearing — whales, earthquakes
Ultrasonic	> 20 000 Hz (> 20 kHz)	Bats, SONAR, medical imaging — applications in Subtopic 4
Ultrasonic vs audible (same medium)	Same speed, higher f, shorter $\lambda$	From $v = f\lambda$ : $v$ is medium-set; higher $f \Rightarrow$ shorter $\lambda$ Distractors pair higher frequency with higher SPEED — wrong; speed is set by the medium.
Speed of sound in air ( $20°$ C)	$\approx 340$ m/s	Standard round number — memorise
Speed of sound in water ( $20°$ C)	$\approx 1500$ m/s	Tested in 2019: distractors at 330 / 800 / 5000
Speed of sound in steel	$\approx 5000$ m/s	Solid > liquid > gas
Mach number	object speed / sound speed	Compares object's speed to local sound speed
Mach < 1	Subsonic	Most everyday motion (cars, propeller aircraft)
Mach = 1	Sonic / transonic	At the speed of sound — sonic boom region
Mach > 1	Supersonic	Faster than sound (fighter jets, Concorde) NDA 2017 tested exactly this — Mach > 1 means supersonic.
Mach > 5	Hypersonic	Re-entry vehicles, scramjets
Decibel (dB)	log scale of intensity ratio	Unit of intensity LEVEL — NOT a unit of frequency or amplitude
Richter scale	log scale of earthquake energy	Devised 1935 by C.F. Richter; no upper limit (though > 9.5 is rare)

The audible-range endpoints (20 Hz, 20 kHz) and the speed-in-water number (

\approx 1500

m/s) are the most-tested rows — they appear almost yearly.

Common traps

dB measures intensity LEVEL — not frequency, not amplitude

Decibel is a logarithmic ratio of two intensities (or two powers). It is a unit of intensity LEVEL only. Frequency uses Hz, s⁻¹, min⁻¹; amplitude uses Pa (pressure) or m (displacement). Any "which is NOT a unit of frequency" question puts dB as the answer.

3 Hz means 3 cycles per second — full cycles, not half or quarter

Hz is defined as one COMPLETE cycle per second. 3 Hz = 3 complete cycles per second, NOT 6 cycles and NOT 1.5 cycles.

Pressure dependence trap — P only matters via T

"Pressure doubled, speed doubles" is the wrong intuition. The formula

v = \sqrt{\gamma P/\rho}

hides the fact that at constant temperature

P

and

\rho

are proportional, so the ratio is fixed. Speed only changes through TEMPERATURE:

v \propto \sqrt{T}

Frequency does NOT change the speed of sound

A 100 Hz sound and a 10 kHz sound travel at the same speed in the same air. Frequency only changes the WAVELENGTH (

\lambda = v/f

) — the same medium-set speed is shared.

Solid > Liquid > Gas (elasticity wins over density)

Naively you might expect dense materials to be slower, but for sound speed elasticity dominates: steel

\approx 5000

m/s, water

\approx 1500

m/s, air

\approx 340

m/s. The ordering is monotone.

Audible range: 20 Hz to 20 kHz — NOT 0 Hz to 20 kHz

Distractors often use "0 – 200 Hz" or "200 – 20 000 Hz" or "2 000 – 20 000 Hz" to test whether you remember the LOWER endpoint (20 Hz). Below 20 Hz is infrasonic — you feel it as vibration but don't hear it as a tone.

Speed of sound in water $\approx 1500$ m/s, NOT 5000 m/s (that's steel)

Common distractor swaps water and steel speeds. Water sits in the middle: 1500 m/s. Steel

\approx 5000

m/s. Air

\approx 340

m/s.

Mach > 1 is SUPERsonic, not SUBsonic

Subsonic = slower than sound (Mach < 1). Supersonic = faster than sound (Mach > 1). Hypersonic kicks in around Mach 5. Easy to flip under exam pressure.

Ultrasonic does NOT travel faster than audible sound

Higher frequency does NOT imply higher speed — speed is set by the medium (this is the Subtopic 2 result). From

v = f\lambda

: higher

f

only shrinks

\lambda

;

v

is fixed.

What Sound DOES — Reflection, Echo, Reverberation, Beats

Learn this subtopic in the notes

Echo — a single distinct reflection

Minimum distance for a distinct echo

d_\text{min} = \dfrac{v \, t_\text{persistence}}{2}

$v$ speed of sound in the medium (m/s)
$t_\text{persistence}$ ear's persistence threshold $\approx 0.1$ s
$d_\text{min}$ minimum reflector distance (m)

Beats — periodic loud/soft from two close frequencies (interference)

Beat frequency

f_\text{beat} = |f_1 - f_2|

$f_\text{beat}$ number of beats per second (Hz)
$f_1, f_2$ the two nearly-equal source frequencies (Hz)

What sound CAN and CANNOT do — the properties checklist

Property / behaviour	Sound?	Why
Reflection (echoes)	Yes	All waves reflect off a hard boundary
Refraction	Yes	Speed changes between media $\Rightarrow$ wave bends
Diffraction	Yes	Bends around obstacles when obstacle size $\approx \lambda$
Interference (beats)	Yes	Two waves superpose — alternating loud/soft
Resonance	Yes	Forced oscillation at the natural frequency
Doppler effect	Yes	Observed pitch shifts with source/observer motion
Polarization	NO	Polarization requires a TRANSVERSE wave; sound is longitudinal The single most-tested NDA trap — "polarization applies to sound" is always WRONG.
Travel through vacuum	NO	No medium $\Rightarrow$ no molecular collisions $\Rightarrow$ no propagation
Ultrasonic obeys all the above the same way	Yes	Ultrasonic = sound above 20 kHz, otherwise identical behaviour

Rows 7 (polarization) and 8 (vacuum) account for the bulk of the bank's "which is NOT correct" distractors. Row 9 catches the "ultrasonic cannot reflect / refract / be absorbed" trap.

Common traps

Ultrasonic obeys the same property rules as audible sound

Ultrasonic = above 20 kHz. Other than the frequency band, it is ordinary sound — it CAN reflect, refract, diffract, get absorbed, AND it cannot polarize / cannot travel in vacuum. A distractor saying "ultrasonic cannot be reflected, refracted, or absorbed" is always WRONG.

Echo is REFLECTION — not refraction, diffraction, or resonance

Refraction is bending across a medium boundary; diffraction is bending around obstacles; resonance is forced oscillation at a natural frequency. An echo is purely a reflection from a hard surface, heard back after a delay.

Round-trip / 2 — sound goes there AND comes back

The formula has a factor of 2 in the denominator because the wave travels the distance twice (source

\to

wall

\to

source). Forgetting the divide-by-2 gives an answer twice as big as the actual reflector distance.

Reverberation is MULTIPLE reflections — not refraction, not diffraction

The defining property is REPEATED REFLECTION inside an enclosed space. Distractors swap reflection for refraction or use "single reflection" (which would be an echo, not reverberation).

Echo vs reverberation — single vs many, distinct vs sustained

Echo: ONE reflection, heard as a SEPARATE event after a clear delay. Needs reflector

\ge 17

m away in air. Reverberation: MANY reflections, heard as CONTINUOUS persistence. Lives in halls/auditoriums where surfaces are close enough that reflections overlap.

Beats need NEARLY equal frequencies — not equal, not far apart

Equal frequencies (

f_1 = f_2

) give CONSTANT amplitude — no beats. Far-apart frequencies give two distinct tones — no beats. Beats only appear when

|f_1 - f_2|

is small enough (typically < 20 Hz) for the pulsing to be heard as separate maxima.

Beat formula gives MAGNITUDE — the sign is ambiguous

From beat-count alone you cannot tell which source is higher. If you hear 4 beats/s against a 440 Hz reference, the string is either 444 Hz or 436 Hz — extra info is needed (e.g. retune slightly and see if beats speed up or slow down).

How We USE Sound — SONAR, Transducers, Musical Instruments

Learn this subtopic in the notes

SONAR, bats, medical imaging — applications of ultrasonic

Acronym / use	Wave type	Application / setting
SONAR	Ultrasonic (sound)	Sound Navigation And Ranging — underwater distance / submarine / sea-depth SONAR uses ultrasonic, NOT audible sound — easy distractor.
RADAR	Radio waves (EM)	RAdio Detection And Ranging — aircraft / weather, works through air
LIDAR	Light / laser (EM)	LIght Detection And Ranging — surveying, autonomous vehicles, atmospheric science
Bats / dolphins	Ultrasonic	Echolocation — emit ultrasonic, receive reflected echo, infer obstacle position
Medical sonography / ultrasound imaging	Ultrasonic	Pulse + echo through soft tissue — pregnancy scans, organ imaging
Industrial: defect detection, drilling	Ultrasonic	Reflections inside metal reveal cracks; high-frequency vibration drills hard materials
Ultrasonic cleaning	Ultrasonic	High-frequency vibrations in a liquid bath dislodge contaminants from delicate parts

All rows 4–7 work by the same principle as SONAR: emit pulse, measure echo, infer geometry. The only difference is medium.

Microphone, loudspeaker — converting between acoustic and electrical

Device	Input	Output
Microphone	Sound waves (mechanical pressure)	Electrical signal NDA 2022 Sep tested exactly this — distractor swaps sound $\leftrightarrow$ microwaves.
Loudspeaker	Electrical signal	Sound waves (mechanical pressure)
Piezoelectric crystal	Electrical signal (or mechanical stress)	Mechanical vibration (or electrical signal)

The microphone and loudspeaker are essentially the same device run in opposite directions. The piezoelectric crystal works both ways — it's how SONAR and medical-imaging probes generate ultrasonic pulses.

Musical instruments — how wind, string, and percussion produce notes

Instrument family	Vibrating element	Pitch determined by
Wind (flute, clarinet, etc.)	Vibrating air column inside (and outside) the tube	Tube length + open holes (sets the standing-wave wavelength) NDA 2023 Apr trap — loudness comes from AMPLITUDE / intensity of the air column's oscillation, NOT from "momentum of waves on the blowing jet".
Stringed (guitar, violin)	Vibrating string coupled to a resonance box	String length / tension / mass per unit length
Percussion (drum, tabla)	Vibrating membrane or solid body	Membrane tension + size

In all three families, loudness is set by the AMPLITUDE of the vibrating element — bigger displacement = louder. Trap-aware row is the flute.

Common traps

SONAR uses ULTRASONIC, not audible sound

The instinct "SONAR = SOund + NAvigation, so it's sound" is right — but the relevant kind of sound is ULTRASONIC, not audible. Distractor ("audible-range sound") catches students who don't make this distinction.

Bats use ULTRASONIC, not radio waves or microwaves

Bats are biological — they emit and detect sound, not radio waves. Their echolocation calls are in the ultrasonic range (typically 20–100 kHz). RADAR (radio) and microwave-based echolocation belong to technology, not bats.

Microphone is sound $\to$ electrical, NOT the other way around

Distractors swap input and output, or replace "sound" with "microwaves". Microphone takes acoustic energy in, gives electrical energy out — the SPEAKER is the reverse.

Flute loudness comes from amplitude — NOT momentum, NOT arrival time

Arrival time of the jet pulses sets PITCH (frequency of the air column's oscillation). AMPLITUDE of the air column's oscillation sets LOUDNESS (intensity). "Momentum of waves on the blowing jet" is not how loudness is determined — that wording is a deliberate NDA distractor.

Sound formulas

Foundations: What Sound Is and How We Hear It

The human ear — anatomy chain that converts pressure to nerve impulses

Common traps

How We Measure Sound — v = fλ, Speed, and the Frequency Bands

Frequency, period, wavelength — and v = fλ

Speed of sound depends on the MEDIUM — not on f, not on P (at constant T)

Bands and scales — audible / infra / ultrasonic, Mach, sound speeds, decibel, Richter

Common traps

What Sound DOES — Reflection, Echo, Reverberation, Beats

Echo — a single distinct reflection

Beats — periodic loud/soft from two close frequencies (interference)

What sound CAN and CANNOT do — the properties checklist

Common traps

How We USE Sound — SONAR, Transducers, Musical Instruments

SONAR, bats, medical imaging — applications of ultrasonic

Microphone, loudspeaker — converting between acoustic and electrical

Musical instruments — how wind, string, and percussion produce notes

Common traps

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