PhysicsICSE Class 10 · Vibrations and Resonance

Resonance: Meaning, Experiments, Uses and Dangers (ICSE Class 10)

Updated 15 October 2026 · Fact-checked

Resonance is a special case of forced vibrations: when the frequency of an applied periodic force equals the natural frequency of a body, the body vibrates with a very large amplitude. It explains the loud sound of an air column over a tuning fork, a paper rider jumping off a wire, and why soldiers break step on bridges.

Notice that only when the force's frequency equals the natural frequency does the amplitude become large and the sound loud.

Illustration drawn for QuestionBuddy.

Understand Resonance: Meaning, Demonstrations and Uses

Start from forced vibrations. When a periodic force acts on a body, the body is forced to vibrate at the frequency of the force. Usually its amplitude is small, because the force keeps pushing at the 'wrong' moments compared with the body's own rhythm.

Resonance. If the frequency of the applied force is made equal to the natural frequency of the body, every push arrives at just the right moment. Energy builds up from cycle to cycle and the body vibrates with a very large amplitude. This is resonance.

A full examination answer contains four key phrases:
1. a periodic force is applied (forced vibration);
2. the frequency of the applied force…
3. …equals (matches) the natural frequency of the body;
4. so the body vibrates with maximum (large) amplitude, giving a loud sound.

Resonance is a special case of forced vibrations. All resonance is forced vibration, but forced vibration becomes resonance only when the two frequencies match.

Forced vibrations	Resonance
Applied frequency differs from the natural frequency	Applied frequency equals the natural frequency
Amplitude small	Amplitude very large
Sound feeble (unless a large surface is used)	Sound loud
Body vibrates slightly out of step with the force	Body vibrates in step with the force

Demonstration 1: resonance in an air column. Hold a vibrating tuning fork over the open mouth of a tall tube (or a burette) containing water. Lower the water level slowly. At one particular length of the air column a loud sound is heard: the natural frequency of the air column has become equal to the frequency of the fork. It is the air column that resonates, not the water or the glass. The natural frequency of an air column increases as its length decreases, so a fork of higher frequency resonates with a shorter air column.

Demonstration 2: pendulums on a common string. Several pendulums of different lengths hang from a horizontal string stretched between rigid supports. Set one (the driver) swinging. Through the string it applies a periodic force to all the others. The pendulum of the same length as the driver has the same natural frequency and swings with a large amplitude (resonance); the others swing only slightly (forced vibrations).

Demonstration 3: sonometer wire and paper rider. A wire is stretched over a hollow sound box with a small paper rider on its middle. The stem of a vibrating fork is pressed on the box. If the natural frequency of the wire equals the fork's frequency, the wire vibrates strongly and the rider jumps off. A thicker, longer or slacker wire has a lower natural frequency.

Uses of resonance.

Musical instruments: the air column of a flute or the sound box of a guitar or sitar resonates, making the sound loud.
Tuning a radio: the circuit's natural frequency is adjusted until it equals the frequency of the wanted station (electrical resonance), so that station is received strongly.
Finding an unknown frequency by matching it with a known one.

Dangers of resonance.

Soldiers break step while crossing a bridge: if their marching frequency equalled the natural frequency of the bridge, it could vibrate with a dangerously large amplitude.
A sustained note of the right frequency can shatter a wine glass.
Wind, traffic or earthquakes can set tall buildings and bridges into resonance, so engineers give them natural frequencies far from the likely forcing frequencies and fit dampers.
A washing machine or a car may shake violently at one particular speed, when the drum or engine frequency matches the natural frequency of a panel.

Resonance: Meaning, Demonstrations and Uses: formulas and key facts

Condition for resonance: $f_{applied} = f_{natural}$; Gives maximum amplitude.
Frequency and time period: $f = \frac{1}{T}$; f in Hz, T in s.
Wavelength of the sound: $v = f λ$; Speed of sound in air about 330 to 340 m/s.
Resonance in three experiments: Air column over a fork the air column resonates, shorter column for a higher-frequency fork
Pendulums on a string the pendulum of the same length as the driver resonates
Wire on a sound box the paper rider jumps off when the wire's natural frequency equals the fork's; Always name the body whose natural frequency matches.

Air column over a fork	the air column resonates, shorter column for a higher-frequency fork
Pendulums on a string	the pendulum of the same length as the driver resonates
Wire on a sound box	the paper rider jumps off when the wire's natural frequency equals the fork's

How to solve Resonance: Meaning, Demonstrations and Uses questions

Most resonance questions ask you to identify, explain or predict. A short checklist covers them.

1Identify the driver (fork, pendulum, marching soldiers, wind) and the driven body (air column, other pendulum, wire, bridge).
2Ask: does the driver's frequency equal the driven body's natural frequency? If yes, resonance (large amplitude); if no, forced vibrations (small amplitude).
3In an explanation, use all four key phrases: periodic force, frequency of the applied force, equals the natural frequency, large amplitude.
4For a change of fork, use: higher frequency needs a shorter air column, or a shorter, tighter or thinner wire.
5For numbers, use $f = \frac{1}{T}$ (or vibrations ÷ time) and $v = f λ$ , converting rpm or steps per minute into Hz.

Resonance: Meaning, Demonstrations and Uses 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.

Filling a bottle at a tap

Suppose you fill a tall steel water bottle at a tap and listen. The gurgling sound rises steadily in pitch, and at certain moments one note rings out loudly.

What is resonating, and why does the pitch rise?

Try it first, then show the solutionSolution

The splashing water gives a jumble of frequencies; the air column above the water resonates at its own natural frequency, so that note is loud.
As the bottle fills, the air column gets shorter, so its natural frequency (and the pitch) rises.

Answer: The air column above the water; it gets shorter, so its natural frequency rises.

Memory hook: Shorter air, higher note.

A shaking washing machine

Imagine a washing machine whose cabinet rattles violently only when the drum spins at 720 revolutions per minute, and is quiet at higher and lower speeds.

Explain using resonance, and find the frequency involved.

Try it first, then show the solutionSolution

Drum frequency $= \frac{720}{60} = 12$ Hz; the spinning drum applies a periodic force at 12 Hz.
At this speed the forcing frequency equals the natural frequency of the cabinet, so it vibrates with a large amplitude; at other speeds the vibrations are only forced and small.

Answer: Resonance: the drum's 12 Hz matches the cabinet's natural frequency.

Memory hook: Only one speed shakes: that speed is the natural frequency.

Tricks to remember Resonance: Meaning, Demonstrations and Uses

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

Four words for full marks
'Forced, Frequency, Matches Natural, Maximum amplitude' (F-F-MN-MA).
Use it when: Writing a complete definition of resonance.
Square and rectangle
Every square is a rectangle, but not every rectangle is a square: every resonance is a forced vibration, not every forced vibration is resonance.
Use it when: Distinguishing forced vibrations from resonance.
Air, not water
'The air sings, the water only sets the stage': the air column resonates.
Use it when: Air-column questions.
Same length, same swing
Twin pendulums dance together; the rest just shuffle.
Use it when: Pendulum demonstration.

Resonance: Meaning, Demonstrations and Uses: solved examples

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

Example 1: Identifying resonance · 1 mark · MCQBoard level

A body vibrates with its maximum amplitude when:
(a) no external force acts on it
(b) the frequency of the applied force is much higher than its natural frequency
(c) the frequency of the applied force equals its natural frequency
(d) it vibrates in a vacuum

Try it first, then show the solutionSolution

Maximum amplitude occurs at resonance, when the forcing frequency matches the natural frequency.

Answer: (c) the frequency of the applied force equals its natural frequency

Example 2: Defining resonance · 3 marks · Short answerBoard level

(a) Define resonance. (b) Why is resonance called a special case of forced vibrations? (c) Give one use of resonance.

Try it first, then show the solutionSolution

(a) When a body is made to vibrate by a periodic force whose frequency equals its natural frequency, it vibrates with a very large amplitude; this is resonance. (1)
(b) The body is still vibrating under an external periodic force (a forced vibration), but only in the special case where the two frequencies are equal. (1)
(c) Tuning a radio set to a station, or the resonance of the air column in a flute. (1)

Answer: (a) Large-amplitude vibration when the applied frequency equals the natural frequency (b) It is forced vibration with matched frequencies (c) Radio tuning (any one)

Example 3: A tuning fork's period and wavelength · 2 marks · Short answerHarder board level

A tuning fork marked 384 Hz is used to show resonance with an air column. Find (a) its time period in milliseconds, (b) the wavelength of its sound in air, where sound travels at 336 m/s.

Try it first, then show the solutionSolution

(a) $T = \frac{1}{384} \approx 2.6 \times 1 0^{- 3}$ s $= 2.6$ ms. (1)
(b) $λ = \frac{v}{f} = \frac{336}{384} = 0.875$ m. (1)

Answer: (a) About 2.6 ms (b) 0.875 m

Example 4: The pendulum demonstration · 3 marks · Short answerHarder board level

Five pendulums P, Q, R, S and T hang from a tight horizontal string. P and S are each 50 cm long; Q is 30 cm, R is 70 cm and T is 90 cm. P is pulled aside and released.
(a) Which of the other pendulums swings most widely, and why?
(b) What kind of vibrations do Q, R and T perform, and at what frequency?
(c) How does the energy reach the other pendulums?

Try it first, then show the solutionSolution

(a) S: it has the same length as P, so the same natural frequency; the periodic force from P matches it and S resonates. (1)
(b) Forced vibrations, at the frequency of P (not their own), with small amplitude. (1)
(c) Through the common string, which P makes vibrate periodically. (1)

Answer: (a) S, resonance (same length) (b) Forced vibrations at P's frequency (c) Through the common string

Example 5: Why soldiers break step · 2 marks · Short answerHarder board level

Explain why soldiers marching in step are ordered to break step when crossing a suspension bridge. Name the phenomenon they are avoiding.

Try it first, then show the solutionSolution

Marching in step applies a periodic force on the bridge at the marching frequency. If this equals the natural frequency of the bridge, it would vibrate with a very large amplitude and could be damaged. (1)
Breaking step makes the force irregular, so no single frequency can build up: they avoid resonance. (1)

Answer: To avoid resonance between the marching frequency and the bridge's natural frequency

Example 6: Changing the fork over an air column · 3 marks · Short answerHOTS / competency

A 320 Hz fork gives a loud sound over a water-filled tube when the air column is 26 cm long. Taking the natural frequency of the air column as inversely proportional to its length, find the air-column length for a loud sound with (a) a 640 Hz fork, (b) a 260 Hz fork. (c) For which fork must the water level be raised?

Try it first, then show the solutionSolution

(a) $l = 26 \times \frac{320}{640} = 13$ cm. (1)
(b) $l = 26 \times \frac{320}{260} = 32$ cm. (1)
(c) The 640 Hz fork needs a shorter air column, so the water level must be raised. (1)

Answer: (a) 13 cm (b) 32 cm (c) For the 640 Hz fork

Example 7: Case study: wires on sound boxes · 4 marks · Case-basedHOTS / competency

Three steel wires X, Y and Z of the same length and tension are stretched on identical sound boxes, each with a paper rider at its middle. X is the thinnest and Z the thickest. A vibrating fork is placed on each box in turn; the rider jumps off only on Y.
(a) Name the phenomenon and explain why the rider on Y jumps off.
(b) Is the natural frequency of X more or less than that of the fork? Give a reason.
(c) Suggest one change to wire Z (other than its thickness) that could make its rider jump off.
(d) What is the purpose of the hollow sound box?

Try it first, then show the solutionSolution

(a) Resonance: the fork's frequency equals the natural frequency of wire Y, so Y vibrates with a large amplitude and throws the rider off. (1)
(b) More: X is thinner (less mass per unit length), so its natural frequency is higher than Y's, which equals the fork's. (1)
(c) Z's natural frequency is too low; increase its tension or shorten its vibrating length to raise its natural frequency to the fork's. (1)
(d) The box and the air inside are forced to vibrate over a large area, making the sound louder. (1)

Answer: (a) Resonance with Y (b) More, X is thinner (c) Increase tension or shorten the wire (d) To make the sound louder

Where students lose marks in Resonance: Meaning, Demonstrations and Uses

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

Mistake: Calling resonance 'forced vibrations' (or the reverse)
Resonance is the special case where frequencies match; a loud sound at one particular length signals resonance.
Wrong working
Naming the loud sound over the air column 'forced vibrations'.
Right working
'Resonance: the fork's frequency equals the natural frequency of the air column.'
Do this: Loud at one special setting = resonance; slight vibration at any setting = forced vibrations.
Usually costs: Reported by CISCE examiners for 2024 Q7(iii).
Mistake: Leaving out key words
Examiners look for 'natural frequency', 'matches/equals' and 'amplitude increases'.
Wrong working
'Because the frequencies are the same.'
Right working
'The frequency of the fork equals the natural frequency of the air column, so it vibrates with a large amplitude.'
Do this: Use F-F-MN-MA every time.
Usually costs: Reported by CISCE examiners for 2024 Q7(iii) and 2025 Q7(iii).
Mistake: Matching the wrong body
It is the natural frequency of the air column (or wire) that matches, not that of the burette, water, paper rider or wooden box.
Wrong working
'The fork's frequency matches that of the paper rider.'
Right working
'The fork's frequency matches the natural frequency of the wire.'
Do this: Name the body that vibrates strongly.
Usually costs: Reported by CISCE examiners for 2025 Q7(iii) and 2024 Q7(iii).
Mistake: Correct direction, no reason
For a higher-frequency fork the air column must be shorter because a shorter column has a higher natural frequency; the reason carries the mark.
Wrong working
'Decrease.'
Right working
'Decrease, because the natural frequency of an air column increases as its length decreases.'
Do this: Always add 'because…'.
Usually costs: Reported by CISCE examiners for 2024 Q7(iii)(c).

Exam tips

Read sound-box diagrams carefully for differences in thickness, length or tension of the wires; these change the natural frequency.
For 'name the phenomenon', a loud sound at one particular length or a rider jumping off means resonance.
Write 'air column', never 'water column', in resonance-tube answers.
Give one use and one danger of resonance if asked for applications; examiners accept radio tuning and soldiers breaking step.

Practice questions on Resonance: Meaning, Demonstrations and Uses

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
Resonance is a special case of:
(a) free vibrations
(b) forced vibrations
(c) damped vibrations
(d) natural vibrations
Hint
An external periodic force is needed.
Answer
(b) forced vibrations
Q2 · 1 mark · Very short answerBoard level
In the air-column experiment, which part actually resonates with the tuning fork?
Hint
Not the water.
Answer
The air column above the water.
Q3 · 2 marks · Short answerHarder board level
A driver pendulum makes 25 complete swings in 40 s. Find its time period and frequency. What must be true of a second pendulum on the same string if it is to resonate with it?
Hint
$T = \frac{t}{n}$ .
Answer
$T = \frac{40}{25} = 1.6$ s, $f = \frac{1}{1.6} = 0.625$ Hz. The second pendulum must have the same natural frequency, i.e. the same length.
Q4 · 3 marks · Short answerBoard level
Draw and label the arrangement of pendulums on a common string used to demonstrate resonance, and state what is observed.
Hint
Driver and its twin.
Answer
A horizontal string tied tightly between two rigid supports, with several pendulums of different lengths, two of them equal (driver A and B). When A is set swinging, B (same length) swings with a large amplitude (resonance), while the others swing with small amplitudes (forced vibrations).
Q5 · 2 marks · Short answerHarder board level
A troop marches at 108 steps per minute. Find the marching frequency in Hz. Why might this be dangerous on a footbridge whose natural frequency is 1.8 Hz?
Hint
Divide by 60.
Answer
$f = \frac{108}{60} = 1.8$ Hz, equal to the bridge's natural frequency, so marching in step could cause resonance and make the bridge vibrate with a dangerously large amplitude.
Q6 · 2 marks · Short answerHarder board level
A student writes: 'Whenever a body is made to vibrate by a periodic force, it resonates.' Correct the statement, and state two ways in which ordinary forced vibrations differ from resonance.
Hint
Is every forced vibration resonance?
Answer
It resonates only if the frequency of the force equals its natural frequency; otherwise it performs ordinary forced vibrations. Differences: (1) in forced vibrations the applied frequency differs from the natural frequency, in resonance they are equal; (2) Forced vibrations have a small amplitude; resonance gives a very large amplitude (loud sound).
Q7 · 3 marks · Short answerHarder board level
An FM radio station broadcasts at 93.5 MHz. (a) What must be adjusted in the radio to receive it clearly? (b) Name the phenomenon. (c) Find the wavelength of the station's waves. ( $c = 3 \times 1 0^{8}$ m/s)
Hint
Electrical resonance.
Answer
(a) The natural frequency of the tuning circuit, until it equals 93.5 MHz. (b) Resonance (electrical). (c) $λ = \frac{3 \times 1 0 ^{8}}{93.5 \times 1 0 ^{6}} \approx 3.21$ m.
Q8 · 1 mark · Assertion-reasonHarder board level
Assertion (A): A vibrating tuning fork of higher frequency produces a loud sound with a shorter air column.
Reason (R): The natural frequency of an air column increases as its length decreases.
(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
Match natural frequency to fork frequency.
Answer
(c) Both are true, and (R) explains (A).
Q9 · 3 marks · Short answerHOTS / competency
A wine glass has a natural frequency of 880 Hz. A singer holds steady notes of 440 Hz and then 880 Hz near it. (a) Which note could shatter the glass? Explain. (b) Find the wavelength of that note in air (speed 340 m/s). (c) Why does the singer need to hold the note for some time?
Hint
Energy builds up only at resonance.
Answer
(a) The 880 Hz note: it equals the glass's natural frequency, so the glass resonates with an ever-larger amplitude until it may crack; at 440 Hz it only performs small forced vibrations. (b) $λ = \frac{340}{880} \approx 0.386$ m. (c) At resonance energy builds up over many cycles, so the amplitude grows gradually.

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.Condition for resonance?Show answer
Applied frequency equals natural frequency.
2.Amplitude at resonance?Show answer
Maximum (very large).
3.Higher-frequency fork over an air column needs a…Show answer
Shorter air column.
4.Which pendulum resonates with the driver?Show answer
The one of the same length.
5.Why do soldiers break step on a bridge?Show answer
To avoid resonance.

Resonance: Meaning, Demonstrations and Uses: frequently asked questions

What is resonance in physics?

Resonance is the large-amplitude vibration of a body when a periodic force acts on it with a frequency equal to the body's natural frequency.

Why is resonance called a special case of forced vibrations?

In resonance the body is still forced by an external periodic force, but the force's frequency happens to equal the body's natural frequency, so the amplitude becomes very large.

What is an example of resonance in daily life?

Tuning a radio to a station, the loud note of a flute's air column, a glass shattering at a sustained note, and soldiers breaking step on a bridge to avoid it.