ScienceCBSE Class 9 · Sound Waves: Characteristics and Applications

Wavelength, Frequency, Speed, Pitch and Loudness of Sound (Class 9)

Updated 17 October 2026 · Fact-checked

Sound is a longitudinal mechanical wave of compressions and rarefactions that needs a medium. Its wavelength λ is the distance between two consecutive compressions (or rarefactions), its frequency ν (in hertz) is the number of oscillations per second, and its time period is T = 1/ν. The speed is v = λν; it is about 340 m s⁻¹ in air, 1500 m s⁻¹ in water and 5000 m s⁻¹ in steel. Pitch depends on frequency, loudness on amplitude, and the audible range is 20 Hz to 20 kHz.

Understand Wavelength, Frequency, Speed, Pitch and Loudness of Sound

What a sound wave is. Sound is produced by a vibrating object (rubber band, tuning fork, vocal cords, air in a flute) and needs a medium (solid, liquid or gas); the bell-jar experiment shows that it cannot travel through vacuum. The vibrating source pushes particles together to form a compression (higher density) and pulls them apart to form a rarefaction (lower density). Particles only vibrate about their mean positions while the disturbance moves forward. Sound is therefore a longitudinal mechanical wave, and it carries energy.

Quantities describing the wave. Wavelength (λ): the distance between two consecutive crests or two consecutive troughs, that is, one compression plus one rarefaction; unit metre. One oscillation at a fixed point: the density goes from maximum to minimum and back to maximum. Frequency (ν): the number of oscillations per second at a fixed point; unit hertz (Hz) = s⁻¹. Time period (T): the time for one complete oscillation; unit second. T = 1/ν, so a higher frequency means a shorter time period. Amplitude: the largest change in density from the average; a larger amplitude carries more energy. Intensity: sound energy passing through unit area (held perpendicular to the direction of travel) in unit time; it decreases with distance from the source.

Speed. In one time period the wave moves one wavelength, so v = λ/T = λν. Approximate speeds at 15 °C: steel 5000 m s⁻¹, water 1500 m s⁻¹, air 340 m s⁻¹. Sound is fastest in solids, then liquids, slowest in gases. In air it increases with temperature and humidity (about 331 m s⁻¹ at 0 °C and 344 m s⁻¹ at 22 °C). In a given medium the speed does not depend on frequency; a higher frequency simply has a shorter wavelength. When a wave passes from one medium to another, its frequency stays the same, and λ changes with speed. Light arrives almost at once but sound later, so the distance to lightning = speed of sound × delay of the thunder.

Pitch, loudness, timbre. Pitch is how we perceive frequency: a high frequency (whistle, mosquito) sounds shrill, a low frequency (thunder, a lion's roar) sounds deep. Loudness is how we perceive amplitude and intensity, measured in decibels (dB): rustling leaves a few dB, conversation about 60 dB, crackers over 100 dB. Timbre is the quality that makes a flute and a tabla sound different at the same pitch and loudness; it comes from the pattern of overtones above the fundamental. An octave is a doubling of frequency. Most everyday sounds mix many frequencies; a tuning fork gives nearly one (a tone).

Range of hearing. About 20 Hz to 20 000 Hz (20 kHz), narrowing with age. Below 20 Hz the sound is infrasonic (elephants hear it; earthquakes and volcanoes produce it). Above 20 kHz it is ultrasonic (dogs, cats, bats and dolphins hear it). Noise is unwanted or harmful sound; long exposure above safe limits harms hearing, sleep and health.

Wavelength, Frequency, Speed, Pitch and Loudness of Sound: formulas and key facts

Frequency and time period: $ν = 1 \div T ∣ ν = n u mb er o f osc i l l a t i o n s \div t im e$
Wave equation: $v = λ ν = λ \div T$
Speeds of sound: Air about 340 m s⁻¹ (331 at 0 °C, 344 at 22 °C)
water about 1500 m s⁻¹
steel about 5000 m s⁻¹
Distance to lightning: $D i s t an ce = s p ee d o f so u n d \times t im e d e l a y o f t h e t h u n d er$
Hearing range: 20 Hz to 20 kHz
infrasonic below 20 Hz
ultrasonic above 20 kHz
Perception: Pitch ↔ frequency
loudness ↔ amplitude and intensity
timbre ↔ overtones

How to solve Wavelength, Frequency, Speed, Pitch and Loudness of Sound questions

Use this method for wave and sound numericals.

1Write what is given with units: frequency in Hz (or oscillations and time), wavelength in m, speed in m s⁻¹.
2Convert kHz to Hz (× 1000) and cm or nm to m before substituting.
3Choose the relation: T = 1/ν, v = λν, or distance = v × t for a one-way trip.
4Substitute, solve and write the unit (Hz, s, m, m s⁻¹).
5When the wave enters another medium, keep the frequency and change only the wavelength using the new speed.
6Check that λ is smaller for a higher frequency in the same medium.

Wavelength, Frequency, Speed, Pitch and Loudness 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.

How far away is the storm?

Suppose you see a lightning flash and hear the thunder 6 seconds later on a day when the speed of sound is 340 m s⁻¹.

Estimate the distance of the lightning and explain why you see the flash first.

Try it first, then show the solutionSolution

Light travels so fast that the flash is seen almost at once, whereas sound takes a measurable time.
Distance = speed × time = 340 × 6 = 2040 m, about 2 km.

Answer: About 2040 m (2 km); light travels far faster than sound.

Memory hook: Flash first, thunder later.

Why a thin rubber band sounds higher

Suppose a student stretches a thin rubber band and a thick one on a box and plucks both.

Which gives the higher pitch and what is the link with frequency and time period?

Try it first, then show the solutionSolution

The thin, tight band vibrates faster, so it has the higher frequency and the higher pitch.
A higher frequency means a shorter time period, since T = 1/ν.
The thick, loose band vibrates more slowly, giving a lower frequency, longer period and a deeper note.

Answer: The thin band has the higher pitch because it has the higher frequency and shorter period.

Memory hook: Fast shake, high note.

Tricks to remember Wavelength, Frequency, Speed, Pitch and Loudness of Sound

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

v is the lambda-nu product
Speed = wavelength × frequency. In one second ν waves pass, each λ long.
Use it when: Any wave numerical.
Pitch = frequency, loudness = amplitude
Higher pitch needs a higher frequency; louder needs a bigger amplitude. The two are independent.
Use it when: Pitch and loudness reasoning.
Solid, liquid, gas: fast, medium, slow
Steel 5000, water 1500, air 340 m s⁻¹, in that order.
Use it when: Comparing speeds in media.
Frequency is the boss
When sound passes into a new medium, the frequency stays and the wavelength adjusts to the new speed.
Use it when: Changes of medium.

Wavelength, Frequency, Speed, Pitch and Loudness of Sound: solved examples

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

Example 1: Frequency, period and wavelength · 3 marks · Short answerBoard level

A tuning fork vibrates at 200 Hz and the speed of sound in air is 340 m s⁻¹. Find (a) its time period, (b) the wavelength, and (c) the number of oscillations in 0.25 s.

Try it first, then show the solutionSolution

(a) T = 1 ÷ ν = 1 ÷ 200 = 0.005 s. (1)
(b) λ = v ÷ ν = 340 ÷ 200 = 1.7 m. (1)
(c) Number of oscillations = ν × t = 200 × 0.25 = 50. (1)

Answer: (a) 0.005 s; (b) 1.7 m; (c) 50 oscillations.

Example 2: Lightning and thunder · 3 marks · Short answerBoard level

A flash of lightning is followed by thunder 6 s later. Take the speed of sound as 340 m s⁻¹.
(a) Find the distance of the lightning. (1)
(b) Why is the flash seen before the thunder is heard? (1)
(c) The next flash gives a delay of 3 s. Is the storm approaching or receding, and how far is it now? (1)

Try it first, then show the solutionSolution

(a) d = 340 × 6 = 2040 m. (1)
(b) Light travels extremely fast, so it reaches us almost at once; sound is far slower. (1)
(c) The delay has shortened from 6 s to 3 s, so the storm is approaching; now d = 340 × 3 = 1020 m. (1)

Answer: (a) 2040 m; (b) light is much faster; (c) approaching, 1020 m.

Example 3: The same note in air, water and steel · 5 marks · Long answerHarder board level

A note of frequency 500 Hz travels through air (340 m s⁻¹), water (1500 m s⁻¹) and steel (5000 m s⁻¹).
(a) Find the wavelength in each. (3)
(b) What happens to the frequency when the sound passes from air into water? (1)
(c) How many times faster is sound in water than in air (to one decimal place)? (1)

Try it first, then show the solutionSolution

(a) Air: λ = 340 ÷ 500 = 0.68 m. Water: λ = 1500 ÷ 500 = 3.0 m. Steel: λ = 5000 ÷ 500 = 10 m. (3)
(b) The frequency stays 500 Hz; only the wavelength changes because the speed changes. (1)
(c) 1500 ÷ 340 = 4.4 times faster. (1)

Answer: (a) 0.68 m, 3.0 m, 10 m; (b) unchanged at 500 Hz; (c) 4.4 times.

Example 4: A tuning fork and an octave · 5 marks · Long answerHarder board level

A tuning fork completes 1280 oscillations in 5 s. Take the speed of sound as 340 m s⁻¹ unless stated.
(a) Find its frequency. (1)
(b) Find its time period (to two significant figures). (1)
(c) Find the wavelength of the sound in air. (1)
(d) On a warmer day the speed of sound is 344 m s⁻¹. Find the new wavelength. (1)
(e) A fork one octave higher is sounded at 340 m s⁻¹. Find its frequency and wavelength. (1)

Try it first, then show the solutionSolution

(a) ν = 1280 ÷ 5 = 256 Hz. (1)
(b) T = 1 ÷ 256 = 0.0039 s (3.9 × 10⁻³ s). (1)
(c) λ = 340 ÷ 256 = 1.33 m. (1)
(d) λ = 344 ÷ 256 = 1.34 m (the wavelength is slightly longer as the speed has increased). (1)
(e) An octave is a doubling: ν = 512 Hz, and λ = 340 ÷ 512 = 0.66 m. (1)

Answer: (a) 256 Hz; (b) 0.0039 s; (c) 1.33 m; (d) 1.34 m; (e) 512 Hz and 0.66 m.

Example 5: Wavelengths at the edges of hearing · 4 marks · Case-basedHOTS / competency

The audible range is 20 Hz to 20 000 Hz and the speed of sound in air is 340 m s⁻¹.
(a) Find the wavelengths of sound at 20 Hz and at 20 000 Hz. (1)
(b) Classify 15 Hz, 440 Hz and 50 kHz as infrasonic, audible or ultrasonic. (1)
(c) A dog whistle sounds at 30 kHz. Find its wavelength in cm. (1)
(d) Why can we not hear the dog whistle, and what hears it? (1)

Try it first, then show the solutionSolution

(a) At 20 Hz: λ = 340 ÷ 20 = 17 m. At 20 000 Hz: λ = 340 ÷ 20 000 = 0.017 m = 1.7 cm. (1)
(b) 15 Hz is infrasonic (below 20 Hz); 440 Hz is audible; 50 kHz is ultrasonic (above 20 kHz). (1)
(c) λ = 340 ÷ 30 000 = 0.0113 m = 1.13 cm (about 1.1 cm). (1)
(d) 30 kHz is above 20 kHz, beyond the range of human hearing; dogs (and cats and bats) can hear ultrasonic sounds. (1)

Answer: (a) 17 m and 1.7 cm; (b) infrasonic, audible, ultrasonic; (c) 1.13 cm; (d) above our range, dogs can hear it.

Where students lose marks in Wavelength, Frequency, Speed, Pitch and Loudness of Sound

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

Mistake: Not converting kHz to Hz.
The prefix is dropped in the substitution.
Wrong working
λ = 340 ÷ 30 = 11.3 m for a 30 kHz whistle
Right working
λ = 340 ÷ 30 000 = 0.0113 m
Do this: Write the frequency in Hz first.
Usually costs: 2 marks.
Mistake: Confusing pitch with loudness.
A high-pitched sound is wrongly called loud.
Wrong working
A shrill whistle has a large amplitude.
Right working
Shrill means high frequency (pitch); loud means large amplitude.
Do this: Pitch: frequency. Loudness: amplitude.
Usually costs: 1 mark.
Mistake: Changing the frequency when sound enters another medium.
Speed and wavelength both change, so frequency is assumed to change.
Wrong working
In water, 500 Hz becomes 2205 Hz.
Right working
The frequency remains 500 Hz; λ = 1500 ÷ 500 = 3 m.
Do this: The source fixes the frequency.
Usually costs: 1 to 2 marks.
Mistake: Writing that sound travels fastest in gases.
Air is the most familiar medium.
Wrong working
Sound is fastest in air and slowest in steel.
Right working
Sound is fastest in solids and slowest in gases.
Do this: Steel > water > air.
Usually costs: 1 mark.
Mistake: Calling sound a transverse wave.
The wave drawing looks like a transverse wave.
Wrong working
Sound is a transverse wave of crests and troughs.
Right working
Sound is a longitudinal wave of compressions and rarefactions; the graph of density against distance has crests and troughs.
Do this: Particles move along the direction of travel.
Usually costs: 1 mark.

Exam tips

Write the relation v = λν (and T = 1/ν) before substituting, with SI units throughout.
State the medium and use its speed of sound; say 'take v = 340 m s⁻¹' if not given.
Explain pitch and loudness by naming frequency and amplitude respectively.
For a graph of density against distance, label a compression, a rarefaction and one wavelength.
For 'speed in different media' give the three values and the order solids > liquids > gases.

Practice questions on Wavelength, Frequency, Speed, Pitch and Loudness 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 · 2 marks · Very short answerBoard level
State which physical property of a sound wave decides (a) its pitch, (b) its loudness. What happens to the loudness of a sound as you move away from the source?
Hint
Frequency and amplitude.
Answer
(a) Pitch depends on frequency; (b) loudness depends on amplitude (and intensity) (1 mark). Loudness decreases with distance because the sound energy spreads over a larger area, so the intensity falls (1 mark).
Q2 · 3 marks · Short answerHarder board level
A sound wave has a frequency of 680 Hz and a wavelength of 0.5 m. Find (a) its speed, (b) its time period, and (c) the time it takes to travel 2.04 km at this speed.
Hint
Use v = λν first.
Answer
(a) v = λν = 0.5 × 680 = 340 m s⁻¹ (1 mark). (b) T = 1 ÷ 680 = 0.00147 s (1 mark). (c) 2.04 km = 2040 m, so t = 2040 ÷ 340 = 6 s (1 mark).
Q3 · 2 marks · Assertion-reasonBoard level
Assertion (A): In a given medium, a sound of higher frequency has a shorter wavelength. Reason (R): The speed of sound in a given medium is constant and v = λν. Choose: (a) A and R both true, R explains A; (b) A and R both true, R does not explain A; (c) A true, R false; (d) A false, R true.
Hint
If v is fixed, how does λ change with ν?
Answer
(a). With v constant, λ = v ÷ ν, so a higher frequency means a shorter wavelength.
Q4 · 3 marks · Short answerHarder board level
Two tuning forks have frequencies 256 Hz and 512 Hz and are struck equally hard. Take the speed of sound as 340 m s⁻¹. (a) Which gives the higher pitch? (b) Find the wavelength of each. (c) How do the loudness, the speed and the time period compare?
Hint
Same medium, so the same speed.
Answer
(a) The 512 Hz fork has the higher pitch (1 mark). (b) 340 ÷ 256 = 1.33 m and 340 ÷ 512 = 0.66 m (1 mark). (c) Loudness is similar (same amplitude); the speed is the same in air; the time period of the 512 Hz fork is half that of the 256 Hz fork (1 mark).
Q5 · 4 marks · Case-basedHOTS / competency
A weather station records lightning flashes and the delay to thunder, with sound travelling at 344 m s⁻¹. First flash: delay 6 s. A flash 20 s later: delay 4 s. (a) Find the distance of each flash. (b) Find the speed at which the storm is approaching. (c) By what distance would the answers differ if you used 340 m s⁻¹ for the first flash? (d) Why can the speed of sound be different on another day?
Hint
Use distance = speed × delay for each flash.
Answer
(a) 344 × 6 = 2064 m and 344 × 4 = 1376 m (1 mark). (b) The storm moved 2064 − 1376 = 688 m in 20 s, so the speed = 688 ÷ 20 = 34.4 m s⁻¹ (1 mark). (c) 340 × 6 = 2040 m, which is 24 m less than 2064 m (1 mark). (d) The speed of sound in air rises with temperature and humidity (about 331 m s⁻¹ at 0 °C and 344 m s⁻¹ at 22 °C) (1 mark).

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.What is the SI unit of frequency?Show answer
Hertz (Hz), equal to s⁻¹.
2.What is the audible range of human hearing?Show answer
About 20 Hz to 20 000 Hz.
3.Give the relation between time period and frequency.Show answer
T = 1 ÷ ν.
4.In which kind of medium does sound travel fastest?Show answer
In solids.
5.What unit measures loudness?Show answer
Decibel (dB).
6.What is the speed of sound in water, approximately?Show answer
About 1500 m s⁻¹.

Wavelength, Frequency, Speed, Pitch and Loudness of Sound: frequently asked questions

Why can't sound travel through a vacuum?

Sound is a mechanical wave and needs particles of a medium to pass on the compressions and rarefactions. The bell-jar experiment shows the sound fades as air is removed.

Does a loud sound travel faster than a soft sound?

No. The speed in a given medium depends on the medium and its conditions, not on loudness or frequency.

Why does a boy's voice become deeper in adolescence?

The vocal cords lengthen and thicken, vibrate more slowly, and so produce a lower frequency.

What is timbre?

The quality that lets us tell a flute from a tabla at the same pitch and loudness; it comes from the pattern of overtones.

What is an octave?

A doubling of frequency.