PhysicsICSE Class 10 · Loudness, Pitch and Quality of Sound

Loudness and Intensity of Sound: Factors, Decibels and Noise Pollution (ICSE Class 10)

Updated 15 October 2026 · Fact-checked

Loudness is the sensation by which the ear tells a loud sound from a faint one; it is subjective. Intensity is the sound energy passing per second through unit area normal to the sound, in W m⁻²; it is objective. Loudness grows with amplitude, vibrating area and nearness to the source. Sound level is expressed in decibels (dB).

Understand Loudness and Intensity of Sound

Loudness. Loudness is the characteristic of sound by which a loud sound is distinguished from a faint (soft) one, both having the same pitch and quality. It is a sensation, so it is subjective: the same sound may seem loud to one person and less loud to another whose hearing is weaker.

Intensity. The intensity of sound at a point is the amount of sound energy passing per second through unit area held perpendicular to the direction in which the sound travels:

$I = \frac{E}{t \times area}, unit: J s^{- 1} m^{- 2} = W m^{- 2} .$

Intensity is a physical quantity that can be measured by an instrument; it is objective and does not depend on the listener.

Loudness vs intensity.

Loudness	Intensity
A sensation in the ear	A physical quantity
Subjective: depends on the listener	Objective: same for every listener
Cannot be measured directly	Measured in W m⁻²
Depends on intensity and on the sensitivity of the ear	Depends only on the sound wave

Loudness increases with intensity, but the ear is not equally sensitive at all frequencies (it is most sensitive at a few kHz), so two sounds of equal intensity but different frequency may not seem equally loud.

Factors on which loudness depends.
1. Amplitude of vibration. Intensity is proportional to the square of the amplitude, $I \propto A^{2}$ . Striking a drum harder increases the amplitude and the sound is louder; tripling the amplitude makes the intensity nine times.
2. Surface area of the vibrating body. A larger vibrating surface sets more air into vibration: a big drum is louder than a small one; a tuning fork pressed on a table sounds louder.
3. Distance from the source. Sound spreads out, so intensity falls with distance; for a small source in open air, $I \propto \frac{1}{d ^{2}}$ . Moving twice as far makes the intensity one quarter.
4. Density of the medium. Sound is louder in a denser medium.
5. Presence of resonating bodies. Sound boxes and air columns that resonate make the sound louder.
6. Motion of the air: wind blowing towards the listener carries the sound better.

Sound level and the decibel. Because the ear responds to an enormous range of intensities, sound level is expressed on a special scale whose unit is the decibel (dB). CISCE requires only the unit, not calculations. Typical levels: rustling leaves about 10 to 20 dB; a whisper about 30 dB; normal conversation about 60 dB; heavy traffic about 80 to 90 dB; a jet engine close by about 120 dB or more, which is painful. A small rise in dB means a large rise in intensity.

Noise and noise pollution. Noise is an unpleasant sound with an irregular waveform; music is pleasant with a regular waveform. Noise pollution is unwanted sound loud enough to disturb or harm people.

Effects of noise pollution	Ways to control it
Headaches, irritation and stress	Silencers on vehicles and machines
Loss of sleep and of concentration	No horns or loudspeakers near hospitals and schools
High blood pressure	Sound-proofing walls, double windows
Temporary or permanent hearing loss after long exposure to loud sound (above about 80 dB)	Planting trees along roads; ear protection for workers

Loudness and Intensity of Sound: formulas and key facts

Intensity: $I = \frac{E}{t \times area}$; Energy per second per unit area normal to the sound; unit W m⁻².
Intensity and amplitude: $I \propto A^{2}$; Doubling the amplitude gives four times the intensity.
Intensity and distance (small source, open air): $I \propto \frac{1}{d ^{2}}$; Twice as far gives one quarter.
Typical sound levels: Rustling leaves about 10 to 20 dB
Whisper about 30 dB
Conversation about 60 dB
Heavy traffic about 80 to 90 dB
Jet engine nearby 120 dB or more; Decibel is the unit of sound level (unit only for ICSE).

Rustling leaves	about 10 to 20 dB
Whisper	about 30 dB
Conversation	about 60 dB
Heavy traffic	about 80 to 90 dB
Jet engine nearby	120 dB or more

How to solve Loudness and Intensity of Sound questions

Loudness questions are mainly explanations and comparisons, with simple ratio work on amplitude and distance.

1For a definition, say loudness is a sensation (subjective) and intensity is energy per second per unit area (objective, W m⁻²).
2For 'why louder', name the factor: larger amplitude, larger vibrating area, shorter distance, denser medium or a resonating body.
3For amplitude changes, square the amplitude ratio: $\frac{I _{2}}{I _{1}} = (\frac{A _{2}}{A _{1}})^{2}$ .
4For distance changes, invert and square: $\frac{I _{2}}{I _{1}} = (\frac{d _{1}}{d _{2}})^{2}$ ; if both change, multiply the two factors.
5For sound level, give the unit decibel (dB); for noise pollution, list effects and controls separately.

Loudness and Intensity of Sound in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Moving away from a speaker

Suppose you stand 3 m from a loudspeaker at a party and find it too loud. You move to 12 m away.

By what factor does the intensity reaching you fall (treat the speaker as a small source in open air)?

Try it first, then show the solutionSolution

$\frac{I _{2}}{I _{1}} = (\frac{3}{12})^{2} = \frac{1}{16}$ .
So the intensity is one-sixteenth of what it was.

Answer: It falls to one-sixteenth.

Memory hook: Four times farther, sixteen times fainter.

Silence zones near hospitals

Imagine your town marks a 'silence zone' with no horns around a hospital, where the sound level outside is otherwise about 85 dB from traffic.

Why is this needed, and name two other ways to cut the noise for patients.

Try it first, then show the solutionSolution

Long exposure to sound above about 80 dB causes stress, sleeplessness and raised blood pressure, which harm recovering patients.
Other controls: sound-proof windows and walls, trees and hedges along the road, silencers on vehicles.

Answer: To protect patients from harmful noise; use sound-proofing and a belt of trees (or vehicle silencers).

Memory hook: Quiet heals.

Tricks to remember Loudness and Intensity of Sound

Short memory aids. Say each one aloud once, then use it on a question the same day.

Loudness lives in the ear
Loudness is in your ear (subjective); intensity is in the air (objective).
Use it when: Subjective vs objective.
Square both ways
Amplitude: square it. Distance: flip it and square it.
Use it when: Ratio questions.
Big drum, big sound
More area, more air moved, more loudness.
Use it when: Surface-area factor.
dB is level, Hz is pitch
Decibels for 'how loud', hertz for 'how high'.
Use it when: Units of sound level and frequency.

Loudness and Intensity of Sound: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Unit of sound level · 1 mark · MCQBoard level

The level of a sound is commonly expressed in:
(a) hertz
(b) decibel
(c) newton
(d) watt

Try it first, then show the solutionSolution

Sound level is measured in decibels (dB); hertz is for frequency.

Answer: (b) decibel

Example 2: Loudness against intensity · 3 marks · Short answerBoard level

(a) Define intensity of sound and give its SI unit. (b) Why is loudness called a subjective quantity? (c) Can two sounds of equal intensity seem unequally loud? Explain.

Try it first, then show the solutionSolution

(a) The sound energy passing per second through unit area held normal to the direction of sound; W m⁻². (1)
(b) It is a sensation that depends on the listener's ear as well as on the sound. (1)
(c) Yes: the ear's sensitivity depends on frequency, so equal intensities at different frequencies (or for different listeners) may not seem equally loud. (1)

Answer: (a) Energy per second per unit area; W m⁻² (b) Depends on the listener (c) Yes

Example 3: Calculating intensity · 2 marks · Short answerHarder board level

A microphone of face area $0.15$ m² placed facing a source receives 0.6 J of sound energy in 2 s. Find the intensity of sound at the microphone.

Try it first, then show the solutionSolution

Energy per second $= \frac{0.6}{2} = 0.3$ W. (1)
$I = \frac{0.3}{0.15} = 2$ W m⁻². (1)

Answer: 2 W m⁻²

Example 4: Hitting a drum harder · 2 marks · Short answerHarder board level

A drummer hits a drum so that the amplitude of the skin's vibration becomes three times as large. (a) By what factor does the intensity change? (b) Does the pitch change? Explain.

Try it first, then show the solutionSolution

(a) $I \propto A^{2}$ : $3^{2} = 9$ times. (1)
(b) No: pitch depends on frequency, which is set by the drum skin itself, not on the amplitude. (1)

Answer: (a) 9 times (b) No

Example 5: Intensity at a greater distance · 3 marks · Short answerHOTS / competency

The intensity of sound from a small siren is 0.02 W m⁻² at 5 m. Assuming $I \propto \frac{1}{d ^{2}}$ , find (a) the intensity at 10 m, (b) the distance at which the intensity is one-ninth of its value at 5 m.

Try it first, then show the solutionSolution

(a) $I = 0.02 \times (\frac{5}{10})^{2} = 0.005$ W m⁻². (1½)
(b) One-ninth needs $(\frac{5}{d})^{2} = \frac{1}{9}$ , so $d = 15$ m. (1½)

Answer: (a) 0.005 W m⁻² (b) 15 m

Example 6: Factors of loudness · 3 marks · Short answerHarder board level

Explain, naming the factor involved: (a) a large drum is louder than a small one struck equally hard; (b) a guitar is louder than the same string on a plank; (c) a firecracker sounds fainter from a distant terrace.

Try it first, then show the solutionSolution

(a) Larger surface area of the vibrating body sets more air vibrating. (1)
(b) The resonating sound box (and its air) increases the vibrating area. (1)
(c) Greater distance: the sound energy spreads out, so the intensity falls. (1)

Answer: (a) Surface area (b) Resonating box (c) Distance

Example 7: Case study: two changes at once · 4 marks · Case-basedHOTS / competency

A speaker at a school function produces intensity $I_{0}$ at a student 8 m away.
(a) The volume is turned down so the amplitude of the cone is halved. What is the new intensity at the student?
(b) The student then moves to 4 m from the speaker. What is the intensity now, in terms of $I_{0}$ ?
(c) Is the sound now as loud to her as at first? Comment on whether loudness must be exactly the same.
(d) Give one health effect of long exposure to very loud music.

Try it first, then show the solutionSolution

(a) $I = I_{0} \times (\frac{1}{2})^{2} = \frac{I _{0}}{4}$ . (1)
(b) $I = \frac{I _{0}}{4} \times (\frac{8}{4})^{2} = I_{0}$ . (1)
(c) The intensity is back to $I_{0}$ , so it should seem about as loud; but loudness is subjective, so her perception may differ slightly. (1)
(d) Temporary or permanent hearing loss (or headache, stress). (1)

Answer: (a) $\frac{I _{0}}{4}$ (b) $I_{0}$ (c) About the same, loudness being subjective (d) Hearing loss

Where students lose marks in Loudness and Intensity of Sound

The slips examiners see most often, and what to write instead.

Mistake: Calling intensity subjective or loudness objective
Loudness depends on the listener; intensity is a measurable physical quantity.
Wrong working
'Intensity is subjective because it depends on the ear.'
Right working
'Loudness is subjective; intensity is objective and measured in W m⁻².'
Do this: Ear → loudness; air → intensity.
Usually costs: The 1-mark fill-in or definition.
Mistake: Forgetting to square
Intensity depends on the square of the amplitude and the inverse square of the distance.
Wrong working
Amplitude tripled, so intensity three times.
Right working
Amplitude tripled, so intensity $3^{2} = 9$ times.
Do this: Write $I \propto A^{2}$ before substituting.
Usually costs: The calculation mark.
Mistake: Mixing up loudness and pitch
Loudness depends on amplitude; pitch on frequency.
Wrong working
'The roar of a lion is high because it is loud.'
Right working
'The roar is loud (large amplitude) but low-pitched (low frequency).'
Do this: Loud/soft for loudness; high/low for pitch.
Usually costs: 1 mark.
Mistake: Giving dB as a unit of frequency or intensity
dB is the unit of sound level; intensity is in W m⁻², frequency in Hz.
Wrong working
'Intensity is measured in decibels per square metre.'
Right working
'Intensity: W m⁻². Sound level: dB.'
Do this: Learn the three units together.
Usually costs: 1 mark.

Exam tips

The 2027 specimen paper asks you to pick out traces of the same pitch but different loudness: look for the same spacing (period) but different heights (amplitude).
List factors of loudness as amplitude, surface area, distance, density of medium and resonating bodies.
CISCE asks for the decibel as a unit only; do not attempt dB calculations.
For noise pollution, keep effects and control measures in separate lists.

Practice questions on Loudness and Intensity of Sound

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
Loudness of a sound depends mainly on its:
(a) frequency
(b) amplitude
(c) waveform
(d) wavelength
Hint
Height of the wave.
Answer
(b) amplitude
Q2 · 1 mark · Very short answerBoard level
Fill in the blank: Intensity of sound is an __________ (objective / subjective) quantity.
Hint
Can an instrument measure it?
Answer
Objective.
Q3 · 2 marks · Short answerHarder board level
The amplitudes of two sounds are in the ratio 1 : 4. Find the ratio of their intensities.
Hint
Square the ratio.
Answer
$I_{1} : I_{2} = 1^{2} : 4^{2} = 1 : 16$ .
Q4 · 3 marks · Short answerBoard level
State three effects of noise pollution and three ways to control it.
Hint
Health; sources and barriers.
Answer
Effects (any three): headaches and stress; loss of sleep; loss of concentration; high blood pressure; hearing loss. Controls (any three): silencers on vehicles and machines; banning horns near hospitals and schools; sound-proofing; planting trees along roads; ear protection.
Q5 · 2 marks · Short answerHarder board level
You walk from 8 m to 2 m away from a small, steady source of sound. By what factor does the intensity at your ear change?
Hint
$(\frac{d _{1}}{d _{2}})^{2}$ .
Answer
$(\frac{8}{2})^{2} = 16$ : it becomes 16 times as great.
Q6 · 2 marks · Short answerHarder board level
Give two differences between loudness and intensity.
Hint
Nature and measurement.
Answer
(1) Loudness is a sensation (subjective); intensity is a physical quantity (objective). (2) Loudness cannot be measured directly and depends on the listener's ear; intensity is measured in W m⁻² and is the same for all listeners.
Q7 · 2 marks · Short answerHarder board level
Why is the sound of a sitar louder than that of a single stretched string of the same tension?
Hint
Resonating body.
Answer
The sitar's hollow body and the air in it are forced to vibrate with the strings, giving a large vibrating surface that sets more air vibrating; this increases the loudness.
Q8 · 3 marks · Short answerHOTS / competency
A source's amplitude is doubled. (a) If the listener also moves to twice the distance, what happens to the intensity? (b) What if the listener moves to four times the distance instead? Show working.
Hint
Multiply the amplitude factor by the distance factor.
Answer
(a) $2^{2} \times (\frac{1}{2})^{2} = 1$ : unchanged. (b) $2^{2} \times (\frac{1}{4})^{2} = \frac{1}{4}$ : one quarter.
Q9 · 1 mark · Assertion-reasonHarder board level
Assertion (A): A sound of 120 dB near a jet engine can be painful.
Reason (R): The decibel is the unit of frequency of a sound.
(a) (A) is true and (R) is false.
(b) (A) is false and (R) is true.
(c) Both (A) and (R) are true, and (R) is the correct explanation for (A).
(d) Both (A) and (R) are true, but (R) is not the correct explanation for (A).
Hint
What does dB measure?
Answer
(a) (A) is true; (R) is false: the decibel is the unit of sound level, not frequency.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.SI unit of intensity of sound?Show answer
W m⁻².
2.Unit of sound level?Show answer
Decibel (dB).
3.Intensity when amplitude is doubled?Show answer
Four times.
4.Is loudness subjective or objective?Show answer
Subjective.
5.Typical level of normal conversation?Show answer
About 60 dB.

Loudness and Intensity of Sound: frequently asked questions

What is the difference between loudness and intensity?

Loudness is how loud a sound seems to a listener, so it is subjective. Intensity is the sound energy per second per unit area, measured in W m⁻², so it is objective.

On what factors does the loudness of sound depend?

On the amplitude of vibration, the area of the vibrating surface, the distance from the source, the density of the medium and the presence of resonating bodies.

In what unit is sound level measured?

In decibels (dB). Normal conversation is about 60 dB, while long exposure above about 80 dB can damage hearing.