Sound notes: ICSE Class 10 Physics (Science Paper 1)

1. Reflection of sound and echoes

Sound is reflected by hard, large surfaces and obeys the laws of reflection.
Echo: sound heard after reflection from a distant obstacle, separately from the original sound.
Conditions: (1) the echo must reach the ear at least 0.1 s after the original sound (persistence of hearing); (2) so the reflector must be at least 17 m away in air ( $340 \times 0.1 \div 2$ ); (3) the reflector must be large compared with the wavelength; (4) the sound must be loud enough.
Echo relations: $d = \dfrac{v t}{2}$ , $v = \dfrac{2d}{t}$ , $t = \dfrac{2d}{v}$ .
Between two cliffs, with echoes after $t_{1}$ and $t_{2}$ : distance between the cliffs $= \dfrac{v (t_{1} + t_{2})}{2}$ .

Table of minimum echo distance for three speeds of sound in air
Speed of sound	Minimum echo distance
330 m/s	16.5 m
340 m/s	17 m
350 m/s	17.5 m

Formulas

Distance of a reflector
$d = \frac{v t}{2}$
Minimum distance for an echo
$d_{\min} = \frac{v \times 0.1}{2}$

Key terms

Echo: A sound heard after reflection from a distant obstacle, distinctly after the original sound.
Persistence of hearing: The time, about 0.1 s, for which the sensation of a sound lasts in the ear.

2. Uses of echoes and SONAR

Ultrasound: frequency above 20 kHz; short wavelength, so it travels in a narrow beam with little spreading and is reflected by small objects.
Bats (echolocation), dolphins, fishing boats (shoals), medical ultrasonography (organs, unborn baby; no harmful radiation).
SONAR: transmitter sends an ultrasonic pulse into the sea; receiver detects the echo; $\text{depth} = \dfrac{v t}{2}$ with $v \approx 1500$ m/s in sea water. Also finds submarines, wrecks and icebergs.

Table of SONAR echo times and depths for sound at fifteen hundred metres per second
Echo time (sea water)	Depth
0.4 s	300 m
1.6 s	1200 m
4.0 s	3000 m

Formulas

SONAR
$\text{depth} = \frac{v t}{2}$

Key terms

SONAR: Sound Navigation And Ranging: a method of finding the distance of underwater objects from the echoes of ultrasonic pulses.
Ultrasound: Sound of frequency above 20 kHz, beyond the range of human hearing.

3. Natural, damped and forced vibrations

Natural (free) vibration: at the body’s own natural frequency, which depends on its size, shape, material, tension (pendulum: length); constant amplitude in the absence of resistance.
Damped vibration: amplitude decreases because of friction and air resistance; frequency stays the natural frequency (pendulum in air, struck tuning fork).
Forced vibration: caused by an external periodic force; the body vibrates at the frequency of the force; amplitude usually small (table top under a tuning fork, sound board of a sitar).

Table of frequency and amplitude for the three kinds of vibration
Vibration	Frequency	Amplitude
Natural	Natural	Constant
Damped	Natural	Decreasing
Forced	Of the applied force	Small unless frequencies match

Formulas

Frequency and time period
$f = \frac{\text{number of oscillations}}{\text{time}}, \quad T = \frac{1}{f}$

Key terms

Natural frequency: The frequency at which a body vibrates when it is disturbed and left free.
Damped vibration: A vibration whose amplitude decreases with time because of resistive forces.
Forced vibration: A vibration produced by an external periodic force, at the frequency of that force.

4. Resonance

Resonance: a special case of forced vibration in which the frequency of the applied force equals the natural frequency of the body, giving a very large amplitude.
Demonstration (Barton’s pendulums): pendulums on a common string; the heavy driver forces all the others; only the one of equal length (same natural frequency) swings with a large amplitude.
Useful: radio tuning; air columns and hollow bodies of musical instruments; resonance tube.
Harmful: soldiers break step on bridges; machines on rubber mountings; glass shattered by a sung note; Tacoma Narrows bridge collapse (1940).

Table comparing ordinary forced vibration with resonance
Forced vibration	Resonance
Any applied frequency	Applied frequency = natural frequency
Small amplitude	Very large amplitude
Table top and tuning fork	Equal-length pendulums

Key terms

Resonance: The large-amplitude vibration of a body when an applied periodic force has a frequency equal to its natural frequency.

5. Characteristics of sound; decibel; noise pollution

Loudness (subjective) depends on amplitude: intensity $\propto A^{2}$ ; also on the area of the vibrating body, distance from the source, density of the medium. Intensity (objective) is the sound energy per second per unit area, in W m⁻².
Pitch (subjective) depends on frequency (objective): higher frequency, shriller sound.
Quality / timbre (subjective) depends on the waveform, set by the number and relative strengths of overtones; lets us tell sources apart at equal pitch and loudness.
Decibel (dB): unit of sound level; +10 dB means 10 times the intensity; above about 80–85 dB is harmful over long periods.
Noise pollution: unwanted loud sound; causes stress, sleeplessness, hearing loss; reduce with silencers, trees, sound-proofing, rules on horns and loudspeakers.

Table of characteristics of sound, what each depends on and whether it is subjective or objective
Characteristic	Depends on	Type
Loudness	Amplitude	Subjective
Pitch	Frequency	Subjective
Quality	Waveform	Subjective
Intensity	Energy flow	Objective

Formulas

Intensity and amplitude
$I \propto A^{2}$
Wave equation
$v = f \lambda$

Key terms

Pitch: The characteristic of sound by which a shrill note is distinguished from a flat one; it depends on frequency.
Quality (timbre): The characteristic that distinguishes two sounds of the same pitch and loudness; it depends on the waveform.
Decibel: The unit used to express the level of a sound.

Exam tips

Common mistakes

Forgetting to halve the round-trip distance in echo and SONAR problems.
Using 340 m/s for sound in sea water.
Saying damping lowers the frequency.
Confusing loudness with pitch.
Calling every forced vibration “resonance”.

How marks are usually awarded

Echo numericals: formula d = vt/2 (1), substitution (1), answer with unit (1).
Resonance: definition with “equal frequency” (1), demonstration (1), example (1).
Characteristics: each characteristic with the quantity it depends on (1 each).

1. Reflection of sound and echoes

Formulas

Key terms

2. Uses of echoes and SONAR

Formulas

Key terms

3. Natural, damped and forced vibrations

Formulas

Key terms

4. Resonance

Key terms

5. Characteristics of sound; decibel; noise pollution

Formulas

Key terms

Exam tips

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