Where Mindful Learning Begins
Where Mindful Learning Begins
Complete NCERT Solutions for Chapter 10 of the new Class 9 Science Exploration textbook (CBSE 2026-27) — every Think It Over, Activity, Pause & Ponder, Worked Example, What If, Revise Reflect Refine, and Journey Beyond question on this one page, with full step-by-step working for every numerical.
Sound closes out the Motion, Force and Sound unit by asking how vibrations turn into something we can hear. You'll work through how sound travels as compressions and rarefactions through a medium, why it needs matter to propagate at all, how wavelength and frequency determine pitch while amplitude determines loudness, and how echoes and SONAR use reflection to measure distance. The wave equation v = λν and the echo-distance formula are the two most exam-relevant tools from this chapter.
Sound Waves: Characteristics and Applications takes sound from something you simply hear to something you can measure and reason about. The chapter builds up how sound is produced by vibrations, why it needs a medium to travel as a longitudinal mechanical wave of compressions and rarefactions, and how that wave is described using wavelength, frequency, time period, amplitude and speed — connected by the single equation v = λν. It closes with how sound reflects (echo and reverberation) and how frequencies beyond human hearing — ultrasonic and infrasonic waves — power SONAR, echolocation and medical imaging. Every question is solved here, section by section, exactly as the textbook presents them, with full working for every numerical.
Vibration as the source of every sound, why a medium (solid, liquid or gas) is essential, and how compressions and rarefactions form a longitudinal wave.
Wavelength, frequency, time period, amplitude and speed — and the one equation, v = λν, that ties every numerical in this chapter together.
Echo, reverberation, pitch and loudness, plus ultrasonic and infrasonic waves behind SONAR, echolocation and medical ultrasound.
Compression vs. rarefaction
| Property | Compression | Rarefaction |
|---|---|---|
| Particle density | High (particles crowded together) | Low (particles spread apart) |
| Pressure | Above average | Below average |
| On a density-distance graph | Appears as a crest | Appears as a trough |
Key formulae
where \(v\) = speed of sound, \(f\) = frequency, \(\lambda\) = wavelength, \(T\) = time period. Loudness depends on amplitude; pitch (how high/low a sound seems) depends on frequency.
Speed of sound by medium
| Medium | Relative speed | Why |
|---|---|---|
| Solids | Fastest | Particles are closely packed, transmitting vibrations quickly |
| Liquids | Medium | Particles are less tightly packed than in solids |
| Gases | Slowest | Particles are far apart, so vibrations transfer more slowly |
Range of hearing
| Range | Frequency | Example |
|---|---|---|
| Infrasonic | Below 20 Hz | Elephants, earthquakes |
| Audible (human range) | 20 Hz – 20,000 Hz | Normal human hearing |
| Ultrasonic | Above 20,000 Hz | Bats, dolphins, medical ultrasound |
An echo requires the reflecting surface to be at least about 17.2 m away (based on the speed of sound in air and the persistence of hearing of 0.1 s), so the reflected sound arrives late enough to be heard as distinct from the original.
Answer: No, not directly through space. Outer space is a near vacuum — there is no medium (matter) between the astronauts for sound to propagate through. Sound is a mechanical wave and needs a solid, liquid, or gas to travel, so voices and the clanking sound of metal objects cannot reach one another through the space between them, however loud they are.
In practice, astronauts communicate using radio transmitters and receivers built into their spacesuits — these convert the sound of a voice into electromagnetic signals (which need no medium and travel even through vacuum) and convert the signal back into sound inside the listener's helmet.
If both astronauts happen to be in direct physical contact with the same solid structure (for example, both gripping the same metal handrail), vibrations from a clank could still travel to them through that solid — the same principle tested in Activity 10.3 with the desk.
Answer: bats use echolocation. They emit short, rapid bursts of ultrasonic waves (frequencies above 20 kHz, beyond human hearing) as they fly. These waves travel outward, reflect off nearby objects and prey, and return to the bat as echoes. By sensing the timing, direction, and characteristics of these returning echoes, the bat can determine the distance, position, size, and even movement of obstacles and prey — allowing it to hunt accurately and navigate without colliding into anything, even in complete darkness.
This same idea is explored in detail later in the chapter under Echolocation (Section 10.8.1) and is the natural inspiration behind SONAR, used by ships and submarines underwater.
Observation: plucking the stretched rubber band produces a sound and you can see it vibrating rapidly. Once the rubber band's vibration stops (comes to rest), the sound also stops. Changing the tension (stretching it more or loosening it) changes the pitch of the sound, and plucking it outside the box (held between two fingers, near the ear) produces a much fainter sound than when it was stretched across the box.
Conclusion: sound is produced by vibrations — as long as the rubber band vibrates, sound is produced; once vibration stops, so does the sound. The cardboard box amplifies the sound by vibrating along with the band and pushing more air, which is why the sound is louder with the box than without it.
Observation: bringing the struck tuning fork near the ear, you hear a clear sound. When one of its vibrating prongs is gently touched to a water surface, ripples (waves) form and spread outward from the point of contact.
Conclusion: the ripples on the water surface are direct visual evidence that the prongs of the tuning fork are actually vibrating, even though the vibration is too fast and too small to see with the naked eye. This confirms that the sound produced is caused by these vibrations — supporting the idea that sound is produced by vibrating objects.
Observation: the knocking sound can be heard both with the ear in the air and — often more clearly — with the ear placed directly against the desk.
Conclusion: since the sound reaches the ear even when travelling through the wood of the desk, this shows that sound can also travel (propagate) through solids, not just through air.
Observation: the sound of the spoons tapping is clearly heard both in air and when the spoons are submerged in water and tapped again.
Conclusion: since the sound of the submerged spoons reaches the listener after travelling through the water and then the air above it, this confirms that sound can also propagate through liquids. Together with Activities 10.1–10.3, this establishes that sound can travel through solids, liquids, and gases — but not through a vacuum, where no medium (matter) exists.
Observation: a sharp push-and-pull at one end creates a disturbance — a region where the turns bunch closer together, followed by a region where they spread further apart — that travels along the slinky towards the other end. Repeating the push-and-pull rapidly produces a series of such disturbances travelling one after another. The marked turn itself does not travel along the slinky; it only oscillates back and forth about its own position, parallel to the direction the disturbance is travelling.
Conclusion: the slinky is a physical analogy for how sound moves through a medium — the closely-bunched regions represent compressions (higher density) and the spread-out regions represent rarefactions (lower density). The disturbance (and the energy it carries) travels through the medium, while the particles of the medium themselves only vibrate about their mean positions — exactly the behaviour of a longitudinal sound wave.
Observation: the grains on the sheet visibly move or jump when a loud sound is produced nearby, even though nothing physically touches the sheet or the container. Louder sounds make the grains jump higher.
Conclusion: as the sound wave travels through the air, it reaches the sheet and makes it vibrate, and this vibration causes the grains to move. This shows that sound is a form of energy — the source of sound transfers energy to the surrounding medium, and this energy is carried by the wave until it reaches the sheet and sets it (and the grains) into motion.
Observation: the frequency is lowest for 'Sa' and increases progressively through Re, Ga, Ma, Pa, Dha, Ni, reaching double the starting frequency at the higher 'Sa'.
Pattern in the ratios: when each note's frequency is divided by the frequency of 'Sa', the ratios follow a fixed, recognisable pattern corresponding to the musical scale — and the higher 'Sa' has a ratio of exactly 2, since it is one full octave above the starting note (an octave being defined as a doubling of frequency). This pattern holds whether the notes are sung by voice or generated electronically, since it reflects the mathematical structure of the musical scale rather than the source producing it.
Observation: as the frequency is increased in steps from 100 Hz to 1000 Hz, the sound becomes progressively higher-pitched or 'shriller'. As the frequency is reduced from 50 Hz down towards 20 Hz, the sound becomes progressively lower-pitched or 'deeper', and near 20 Hz it becomes very difficult to hear at all.
Conclusion: this demonstrates that pitch increases with frequency — higher frequency sounds are perceived as higher-pitched. It also demonstrates the lower edge of the human audible range: sound waves with frequency below 20 Hz (infrasonic waves) are generally inaudible to humans.
Answer: sound can be produced by vibrating an object in many different ways, including:
| Instrument | Vibrating part |
|---|---|
| Guitar, sitar, veena, sarangi | Stretched strings |
| Bansuri (flute), shehnai | Column of air inside the hollow pipe |
| Tabla, mridangam, dhol | Stretched membrane (drumhead) |
| Xylophone, glockenspiel | Wooden or metal bars/plates |
| Violin | Strings, set vibrating by friction with the bow |
| Taal (cymbals) | The metal disc itself, when struck |
Answer: (ii) Both A and R are true, and R is the correct explanation of A. Sound is a mechanical wave and needs a material medium (solid, liquid, or gas) to propagate. As air is pumped out of the jar and a near vacuum is reached, there is almost no medium left to carry the sound, so it becomes inaudible even though the bell can still be seen ringing — this directly explains the assertion.
Answer: (iii) A is true, but R is false. It is true that compressions and rarefactions (the disturbance) move through the medium. However, the individual particles of the medium do not move forward with the wave — they only vibrate back and forth about their own mean positions. It is the disturbance and the energy it carries that travel, not the particles themselves, so R does not correctly explain A.
Answer: (ii) Energy carried by sound waves. The particles of the medium (air) near the tuning fork do not themselves travel all the way to your ear — they only oscillate about their mean positions. What actually reaches your ear is the disturbance (the alternating compressions and rarefactions) and the energy it carries, which then causes the air particles near your eardrum, and the eardrum itself, to vibrate.
Method: in the dot-pattern figure, the regions where the dots are bunched closely together represent higher-than-average density — label these C (compression). The regions where the dots are spread further apart represent lower-than-average density — label these R (rarefaction).
Drawing the graph: on the density-vs-distance axes, draw a smooth wave (sine-like curve) that reaches its highest point (crest) directly below each compression (C) region and its lowest point (trough) directly below each rarefaction (R) region, oscillating evenly above and below the horizontal dashed 'average density' line — exactly as shown in Fig. 10.16(b) of the textbook.
Answer: Yes, for a similar tension and stretch, a thinner rubber band generally vibrates faster than a thicker one, because it has less mass per unit length and offers less resistance to being set in motion.
Since the thin band vibrates faster, it has a higher frequency (more oscillations per second) than the thick band. Since frequency and time period are inversely related (\(\nu = 1/T\)), a higher frequency means the thin band has a shorter (smaller) time period than the thick band. The higher frequency of the thin band is also perceived as a higher-pitched sound.
Frequency = 20 Hz means 20 oscillations every second.
From the graph, one complete wave cycle (crest to the next crest) spans 3.0 cm — so the wavelength λ = 3.0 cm.
Sound travels roughly 4.4 times faster in water than in air, and roughly 3.3 times faster in steel than in water — confirming that sound travels fastest in solids, slower in liquids, and slowest in gases.
Since the time difference (about 0.93 s) is much greater than the minimum 0.1 s needed for the ear to distinguish two separate sounds, yes, she would clearly hear two separate sounds — first the sound arriving through the (much faster) steel fence, and then, nearly a second later, the same sound arriving through the air.
The sound must travel to the surface and back within 0.2 s, so:
The reflecting surface must be placed at a minimum distance of 34.3 m.
The depth of the ocean at that location is 3000 m (3 km).
The frequency is 5 Hz and the time period is 0.2 s.
The wavelength of sound in air is 17.2 m at 20 Hz and 1.72 cm at 20 kHz — showing just how enormous the range of wavelengths is across the audible spectrum.
Since light reaches the observer almost instantaneously compared to sound, the entire 5 s delay is (to a very good approximation) the time taken by sound to travel the distance.
The lightning struck about 1.7 km away.
From the graph, the wavelength λ = 50 m.
The wavelength is 50 m, frequency 100 Hz, and time period 0.01 s.
Sound travels to the wall and back in 0.5 s, so:
The wall is 85 m away.
The object is 688.5 m away.
Answer: a musical note is actually a combination of a fundamental frequency and several higher overtones, all produced together and travelling together to reach the listener. If the speed of sound depended on frequency, these different frequency components would travel at different speeds and arrive at the listener staggered in time, even though they started out perfectly in sync at the source.
This would distort the precise timing relationship between the fundamental and its overtones that gives an instrument or voice its characteristic timbre, and it would get progressively worse over larger distances — a singer and an instrument playing together, or a large concert hall audience seated at different distances from the stage, would hear a smeared, out-of-sync, muddled version of the music rather than a clean note. Music would very likely sound unpleasant or garbled rather than rich and pleasant.
The fact that the speed of sound in a given medium depends only on the medium — not on frequency — is exactly what keeps a musical note's waveform shape intact as it travels, which is why this chapter's 'Ready to Go Beyond' box on speed of sound calls this out explicitly.
Possible advantages: humans could sense high-frequency alarms, animal calls, and machinery sounds currently inaudible to us; it could improve navigation in the dark or underwater in a bat- or dolphin-like way; and it could allow richer communication with animals that already use the ultrasonic range.
Possible disadvantages: many everyday devices and machines (electronics, motors, ultrasonic cleaners, certain alarms, and even some animal and insect sounds) already emit ultrasonic frequencies that we currently cannot hear. If our hearing extended into this range, this would add a constant stream of extra, often unwanted, sound to our daily environment — effectively a new and unavoidable form of noise pollution, potentially causing sensory overload, discomfort, or even hearing damage from sources we have never had to shield ourselves from before.
This trade-off — more sensory information versus more noise to filter out — is the same reason expanding any sense (hearing, smell, vision) is rarely a simple 'more is better' upgrade in nature.
Answer: (ii) Sound needs a medium to propagate. This is the defining property of a mechanical wave — it distinguishes sound from waves like light, which are electromagnetic and can travel through a vacuum. Reflection, frequency, and carrying energy are properties shared by many kinds of waves, but the requirement of a medium is specifically what makes sound mechanical.
Answer: (iii) number of compressions per second. Frequency is defined as the number of density oscillations (compressions) passing a fixed point per second, so increasing frequency directly increases this count. Since speed (v = λν) depends only on the medium and stays constant, increasing frequency actually decreases both the wavelength and the time period, not increases them.
The correct answer is (ii) 5 Hz.
Answer: Reverberation, not an echo. The ear needs a minimum gap of about 0.1 s between the original sound and its reflection to perceive them as two separate sounds (an echo). Here the gap is only 0.05 s, which is well below this threshold and falls within the range the chapter defines for reverberation (reflections arriving with a time difference of less than 0.05 s) — so the reflected sound merges with and prolongs the original sound rather than being heard as a distinct, separate echo.
Method: wavelength is read as the distance between two consecutive crests (or troughs) — the graph with fewer, wider oscillations spread across the same distance has the greater wavelength. Amplitude is read as the height of a crest (or depth of a trough) above (or below) the average density line — the graph with the shorter peaks has the smaller amplitude.
Based on the figure, graph (a) — with fewer, wider humps — has the greater wavelength, and graph (b) — with the visibly shorter peaks — has the smaller amplitude.
Method: for waves travelling at the same speed, frequency and wavelength are inversely related (\(\nu = v/\lambda\)) — a shorter wavelength (more oscillations packed into the same distance) means a higher frequency, and a longer wavelength means a lower frequency.
Count the number of complete waves each curve completes over the shown distance: the curve with the most oscillations (shortest wavelength) is A (highest frequency); the curve with the fewest oscillations (longest wavelength) is C (lowest frequency); the remaining, intermediate curve is B.
Method: on a density (y-axis) vs distance in cm (x-axis) graph, draw a smooth wave (sine-shaped curve) that:
Error 1: outer space is a near vacuum, with essentially no medium for sound to propagate through. A real explosion in space would produce no audible sound at all to a distant observer — only the light from the flash would be visible.
Error 2 (even if sound could somehow travel): light travels enormously faster than sound (about 300,000 km/s versus roughly 340 m/s), so light would reach an observer's eyes almost instantly while sound would arrive much later — showing the flash and the sound arriving at the exact same instant is inconsistent with real physics on both counts.
The time period is 0.01 s.
The wreckage is located approximately 3812.5 m (about 3.81 km) below the surface.
The wave takes approximately 0.007 s (about 7 milliseconds) to travel to the obstacle and back.
Thunder takes about 0.2 seconds longer to cover the same distance at 0°C compared to 22°C, since sound travels more slowly in colder air.
Method: first count how many complete compression–rarefaction cycles fit within the marked 8 cm span in the figure, and divide 8 cm by that number to get the wavelength. Based on the pattern shown (two complete wavelengths across the 8 cm span), λ = 4 cm = 0.04 m.
Always start by counting the number of full wave cycles shown in your own printed copy of the figure and dividing the marked distance by that count — if your figure shows a different number of cycles across the 8 cm, recompute λ accordingly before applying ν = v/λ.
Method: read the wavelength of each curve directly as the distance over which it completes one full cycle. Based on the figure, wave A completes two full cycles by the 5.0 cm mark (λA = 2.5 cm) while wave B completes one full cycle over the same span (λB = 5.0 cm).
Wave A has the shorter wavelength and therefore the higher frequency — always double-check which curve completes more cycles across the same span in your own copy of the figure.
Both sounds travel the same distance d to the cliff and back, so \(v = 2d/t\), meaning speed is inversely proportional to time for the same distance.
The ratio of the speed of sound in air to water is 2 : 9 — in other words, sound travels about 4.5 times faster in water than in air, consistent with the real-world values in Table 10.1.
Points to research and include in your article:
Since scheme names and eligibility criteria can change, always check the latest details on official government websites before publishing your article.
Expected result: the phone sounds noticeably louder in the direction the cone opens towards, compared to the phone playing without the cone.
Explanation: without the cone, the phone's speaker sends sound energy spreading out roughly equally in all directions, so the intensity in any one direction is relatively low. The cone acts like a simple megaphone — it channels and redirects that same total sound energy into a narrower beam, concentrating it in one direction and increasing the intensity (and hence the loudness) a listener perceives from within that beam.
Varying the shape: a longer, narrower cone typically concentrates sound into an even narrower, more focused beam (louder but only over a smaller angle), while a wider, shorter cone spreads the same energy over a broader angle (a smaller loudness boost, but audible over a wider area).
Answer: flat, parallel walls and ceilings tend to reflect sound sharply back along a single, predictable path — this can cause distinct echoes, "flutter echoes" (rapid repeated reflections bouncing back and forth), and uneven sound distribution, where some seats receive too much reflected sound and others too little.
Curved surfaces can be carefully shaped (concave or convex, as needed) to reflect and diffuse sound waves so that they spread out and reach the entire audience more evenly, rather than bouncing back as a concentrated beam. Acousticians can design the exact curvature to direct reflected sound towards the audience seating and to control reverberation time, avoiding both echo problems and "dead spots" where sound doesn't reach clearly.
Answer: light travels so much faster than sound (about 300,000 km/s, compared to roughly 340–346 m/s for sound) that, over a distance of only a few hundred metres, the flash of the balloon bursting reaches your eyes essentially instantaneously. This means the time gap you measure between seeing the burst and hearing the 'pop' is — to an excellent approximation — entirely the time taken by sound to travel that distance, letting you calculate the speed of sound simply as distance ÷ time without needing to separately account for the (negligible) travel time of light.
The measured speed you calculate should come out close to the standard value (around 340–346 m/s depending on air temperature and humidity); differences usually come from reaction-time errors in starting/stopping the stopwatch, wind, or inaccuracies in measuring the distance.
General principle to look for while exploring these simulations: the speed of sound in air increases with increasing temperature, because warmer air molecules move faster on average and transmit the compressions of a sound wave from one particle to the next more quickly. The speed of sound also increases slightly with increasing humidity, because water vapour molecules are lighter than the nitrogen and oxygen molecules that make up most of dry air, making humid air very slightly less dense overall and allowing sound to propagate a little faster through it.
Use the PhET sound waves simulation to visually observe compressions and rarefactions and experiment with frequency and amplitude; use Phyphox's Audio Scope and Audio Spectrum tools (also referenced in the 'Threads of Curiosity' box in Section 10.6.1) to measure real frequencies with your own phone; and use MusicLab to explore how sound waves combine and interact.
Sound is a vibration that becomes a travelling disturbance of compressions and rarefactions in a medium — carrying energy but not matter — and every property we can measure about it (wavelength, frequency, time period, amplitude, and speed, tied together by v = λν) explains what we hear as pitch and loudness, why sound reflects as echo or reverberation, and how frequencies beyond our own hearing, from a bat's ultrasonic call to a ship's SONAR ping, let us sense what our ears alone cannot.
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