NDA Physics · Sound

What Sound DOES — Reflection, Echo, Reverberation, Beats

Because sound is a wave, it does what waves do — reflect, refract, diffract, interfere — except polarize. Reflection gives echo (single) and reverberation (multiple); interference of two close frequencies gives beats.

All Sound notes NDA Physics strategy

Why this matters

Now you know what sound IS and how to MEASURE it. What does it DO? Wave behaviours come in two flavours: (1) things sound CAN do because it's a wave (reflect, refract, diffract, interfere, resonate, Doppler) and (2) things it CAN'T do because it's longitudinal (polarize) or mechanical (vacuum). Then the specific applications of reflection — ECHO (single, 17 m rule) and REVERBERATION (many bounces, halls) — and the interference application — BEATS (rate equal to |f₁ − f₂|). 5 PYQs; all EASY or MODERATE except one HARD (the flute-related instrument question is in Subtopic 4).

Concept 1 of 4

What sound CAN and CANNOT do — the properties checklist

Intuition

NDA recycles "which of the following is NOT correct about sound" every other year — the distractor is always one of the canonical wave properties. Memorise this table once: every row is a property that either applies (because sound is a wave) or fails (because sound is longitudinal / mechanical). The two bold-NO rows — POLARIZATION and TRAVEL-THROUGH-VACUUM — are the trap rows that carry almost every distractor.

Definition

Properties sound SHARES with all waves (reflection, refraction, diffraction, interference, resonance, Doppler) — and the two properties it lacks (polarization, propagation through vacuum). Drill the table top-to-bottom; the bold-NO rows are the trap rows.

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.

Practice this conceptself-check · 4 quick reps

From the bank · past-year question

Example 1SoundMODERATE

Which one of the following statements is

\textbf{\text{not}}

correct?

[Q130 · Sep · 2017]

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.

Concept 2 of 4

Echo — a single distinct reflection

Intuition

When you shout at a distant cliff, the sound travels to the cliff, REFLECTS off it, and comes back. If the cliff is far enough away, the reflected sound arrives at your ear AFTER the original has faded — you hear them as two separate sounds, and that's an echo. Too close, and the reflection overlaps the original — you don't perceive an echo at all.

Definition

An echo is the repetition of a sound caused by a SINGLE reflection from a hard surface. Human ears can resolve two sounds as separate only if their arrival times differ by at least about 0.1 s (the persistence-of-hearing threshold). For a reflection to be heard distinctly: the round-trip time must be at least 0.1 s, so the reflecting surface must be at least $d_\text{min} = v \times 0.1 / 2$ away.

Minimum distance for a distinct echo

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

vspeed 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)

Worked example

What is the minimum distance from a wall at which a shouted sound will produce a distinct echo? Take the speed of sound in air as

v = 340

m/s.

Use $d_\text{min} = v \, t_\text{persistence} / 2$ with $t_\text{persistence} = 0.1$ s.
Round trip travel: $v \times 0.1 = 340 \times 0.1 = 34$ m.
Divide by 2 (sound goes there AND comes back): $d_\text{min} = 34/2 = 17$ m.

Answer:

d_\text{min} \approx 17

m (in air at 20°C).

Practice this conceptself-check · 4 quick reps

From the bank · past-year question

Example 2SoundEASY

We hear an echo due to

[Q149 · Apr · 2025]

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.

Concept 3 of 4

Reverberation — sustained sound from many reflections

Intuition

Inside a large hall, sound bounces off the walls, floor, and ceiling — and bounces off them AGAIN, and again. Each bounce arrives at your ear a tiny bit later than the previous one. So instead of hearing the source then one distinct echo, you hear a CONTINUOUS, fading wash of overlapping reflections — sound that PERSISTS for a moment after the source has stopped. That persistence is reverberation.

Definition

Reverberation is the persistence of sound in an enclosed space due to multiple reflections from the surrounding surfaces, overlapping in time. Contrast with echo, which is a single reflection heard distinctly after the original. Reverberation time $T$ is the time taken for the sound intensity to fall by 60 dB (one-millionth of its original power) after the source stops; long $T$ gives a "live" hall, short $T$ a "dry" one. Absorbent materials (curtains, carpets, acoustic panels) reduce reverberation by soaking up reflected energy.

Worked example

Why does clapping in an empty marble hall produce a sustained, lingering sound, while the same clap in a curtained living room dies almost immediately?

Marble walls are HARD and reflect sound efficiently — almost no energy is absorbed per bounce.
Inside the hall, the clap bounces many times — wall to wall, floor to ceiling — and each bounce arrives at your ear with a small delay.
These overlapping reflections add up to a continuous, slowly-decaying wash of sound — long reverberation time.
In a carpeted, curtained room, soft materials ABSORB most of the reflected energy on each bounce — the clap fades in a fraction of a second.

Answer:Marble = hard, reflective → long reverberation. Carpet/curtains = absorbent → reverberation dies quickly.

Practice this conceptself-check · 4 quick reps

From the bank · past-year question

Example 3SoundEASY

Reverberation is a phenomenon associated with a

[Q138 · Sep · 2021]

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.

Drill 1 more on reverberation — sustained sound from many reflections

Concept 4 of 4

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

Intuition

When two sound waves of NEARLY equal frequency are played together, their amplitudes alternately reinforce and cancel as their phases drift in and out of step. You hear a slow PULSING of loudness — "loud, soft, loud, soft...". Each pulse is one beat. The further apart the two frequencies, the FASTER the pulsing; if the frequencies are equal, there are no beats at all. Beats are the audible signature of INTERFERENCE — the same wave behaviour that's row 4 of the properties checklist.

Definition

Beats occur when two sound waves of slightly different (nearly equal) frequencies $f_1$ and $f_2$ interfere. The resulting sound has periodic amplitude variation — alternating maxima (constructive interference) and minima (destructive) — at a rate equal to the difference of the two frequencies. If $f_1 = f_2$ , no beats. If $f_1, f_2$ are far apart, the variation is too fast to perceive as separate pulses.

Beat frequency

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

f_\text{beat}number of beats per second (Hz)
f_1, f_2the two nearly-equal source frequencies (Hz)

Worked example

Two tuning forks of frequencies 256 Hz and 260 Hz are sounded together. How many beats per second does the listener hear?

Beat frequency = $|f_1 - f_2|$ .
Substitute: $|260 - 256| = 4$ Hz.
So the listener hears 4 pulses (beats) per second.

Answer:4 beats per second.

Practice this conceptself-check · 4 quick reps

From the bank · past-year question

Example 4SoundEASY

'Beats' is a phenomenon that occurs when frequencies of two harmonic waves are

[Q91 · Apr · 2021]

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).

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Echo — a single distinct reflection
Minimum distance for a distinct echo
$d_\text{min} = \dfrac{v \, t_\text{persistence}}{2}$
Beats — periodic loud/soft from two close frequencies (interference)
Beat frequency
$f_\text{beat} = |f_1 - f_2|$

Reference tables (1)

What sound CAN and CANNOT do — the properties checklist9 rows

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.

Watch out for (7)

Ultrasonic obeys the same property rules as audible sound
→ What sound CAN and CANNOT do — the properties checklist
Echo is REFLECTION — not refraction, diffraction, or resonance
→ Echo — a single distinct reflection
Round-trip / 2 — sound goes there AND comes back
→ Echo — a single distinct reflection
Reverberation is MULTIPLE reflections — not refraction, not diffraction
→ Reverberation — sustained sound from many reflections
Echo vs reverberation — single vs many, distinct vs sustained
→ Reverberation — sustained sound from many reflections
Beats need NEARLY equal frequencies — not equal, not far apart
→ Beats — periodic loud/soft from two close frequencies (interference)
Beat formula gives MAGNITUDE — the sign is ambiguous
→ Beats — periodic loud/soft from two close frequencies (interference)

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