CBSE Class 9 Science Sound Assignment

1. Sound : Sound is a form of energy which produces a sensation of hearing in our ears. 

2. Source of sound and its propagation : A source of vibration motion of an object is normally a source of sound.

 3. Characteristics of the medium required for the propagation of sound: 

(i) Medium must be elastic so that the medium particles have the tendency to return back to their original positions after the displacement. 

(ii) Medium must have the inertia so that its particles have the capacity to store the energy. The frictional resistance of the medium should be negligible to minimise the loss of energy in propagation. 

4. Types of waves 

(i) Mechanical waves : A mechanical wave is a periodic disturbance which requires a material medium for its propagation. On the basis of motion of particles the mechanical waves are classified into two parts.
(a) Transverse wave (b) Longitudinal wave
(a) Transverse wave : When the particles of the medium vibrate in a direction perpendicular to the direction of propagation of the wave, the wave is known as the transverse wave. For example, waves produced in a stretched string.
(b) Longitudinal wave : When the particles of the medium vibrate along the direction of propagation of the wave then the wave is known as the longitudinal wave. For example sound wave in air.

(ii) Electromagnetic waves : The waves which do not require medium for propagation are called electromagnetic waves these waves can travel through vacuum also. For example, light waves, X-rays. 

5. Characteristics of a sound wave 

(i) Frequency : The number of vibrations per second is called frequency. 
The unit of frequency is hertz 

(ii) Amplitude: The maximum displacement of each particle from its mean position is called amplitude.
The S.I. unit of amplitude is metre (m). 

(iii) Time period: The time taken to complete one vibration is called time period.
Frequency= 1/(Time period) or v = 1/T 

(iv) Wavelength: The distance between two nearest (adjacent) crests or troughs of a wave is called its wavelength. 

(v) Velocity of wave: The distance travelled by a wave in one second is called velocity of the wave (or speed of the wave). The S.I. unit for the velocity of a wave is metres per second (m/s or ms^-1). 

(vi) Pitch : Pitch is the sensation (brain interpretation) of the frequency of an emitted sound and is the characteristic which distinguishes a shrill (or sharp) sound from a grave (or flat) sound. 

(vii) Loudness : It is a measure of the sound energy reaching the ear per second. 

6. Reflection of sound : When sound waves strike a surface, they return back into the same medium. This phenomenon is called reflection. 

7. Laws of reflection : Angle of incidence is equal the angle of reflection. The incident wave, the reflected wave and the normal all lie in the same plane. 

8. Echo : Phenomenon of hearing back our own sound is called an echo. It is due to successive reflection from the surfaces obstacles of large size. 

9. Relation between speed of sound, time of hearing echo and distance of reflection body : If t is the time at which an echo is heard, d is the distance between the source of sound and the reflecting body and v is the speed of sound. The total distance travelled by the sound is 2d.
speed of sound, v = 2d/t or d = vt/2 

10. Conditions for the formation of Echoes
(i) The minimum distance between the source of sound and the reflecting body should be 17.2 metres.
(ii) The wavelength of sound should be less than the height of the reflecting body.
(iii) The intensity of sound should be sufficient so that it can be heard after reflection. 

11. Reverberation : Persistence of sound after its production is stopped, is called reverberation. A short reverberation is desirable in a concert hall (where music is being played) because it gives ‘life’ to sound. Too much reverberation confuses the programmers and must be reduced to reduce reverberation. 

12. Range of Hearing : The audible range of sound for human beings extends from about 20 Hz to 20,000 Hz (one Hz = one cycle/s). Sounds of frequencies below 20 Hz are called infrasonic sound or infrasound. Frequencies higher than 20 kHz are called ultrasonic sound or ultra sound. Ultrasound is produced by dolphins. 

13. Applications of ultrasound : The ultrasound is commonly used for medical diagnosis and therapy, and also as a surgical tool. It is also used in a wide variety of industrial applications and processes. Some creatures use ultrasound for information exchange and for the detection and location of objects. Also some bats and porpoises are found to use ultrasound for navi gation and to locate food in darkness or at a place where there is inadequate light for vision (method of search is called echolocation). 

14. Sonar : SONAR means Sound Navigation Rang-ing. In this sound waves (ultrasonic) are used [microwaves are absorbed by water)]. Sound waves are emitted by a source. These waves travel in water with velocity v. The waves re-flected by targets (like submarine bottom sea) are detected. 

Uses 

(i) The SONAR system is used for detecting the presence of unseen underwater objects, such as a submerged submarine, a sunken ship, sea rock or a hidden iceberg, and locating them accurately. 

(ii) The principle of SONAR is also used in industry of detection of flaws in metal blocks or sheets without damaging them. 

15. Human ear : It is a highly sensitive part of the human body which enables us to hear a sound. It converts the pressure variations in air with audiable frequencies into electric signals which travel to the brain via the auditory nerve.

The human ear has three main parts. Their auditory functions are as follows: 

(i) Outer ear : The outer ear is called `pinna’. It collects the sound from the suri-ounding. The collected sound passes through the auditory canal. At the end of the auditory canal there is a thin membrane called the ear drum or tympanic membrane. When compression of the medium produced due to vibration of the object reaches the ear drum, the pressure on the outside of the membrane increases and forces the eardrum inward. Similarly, the eardrum moves outward when a rarefaction reaches. In this way the ear drum vibrates. 

(ii) Middle ear: The vibrations are amplified several times by three bones (the hammer, anvil and stirrup) in the middle ear which act as levers. The middle ear transmits the amplified pressure variations received from the sound wave to the inner ear. 

(iii) Inner ear: In the inner ear, the pressure variations are turned into electrical signals by the cochlea. These electrical signals are sent to the brain via the auditory nerve, and the brain interprets them as sound.

Question. The oscillations of a pendulum slow down due to the force exerted by
(a) air and friction at the support
(b) air only
(c) friction at the support only
(d) due to gravity.
Answer: A

Question. If a pendulum is allowed to oscillate into a jar containing water, then its time period will
(a) increase
(b) decrease
(c) remain same
(d) can’t say.
Answer: A

Question. If a pendulum is allowed to oscillate in vacuum, then its time period will
(a) decrease
(b) increase
(c) remain same
(d) will not oscillate
Answer: D

Question. Kinetic energy of the bob of a simple pendulum is maximum at the
(a) mean position
(b) extreme left position
(c) extreme right position
(d) half of extreme position.
Answer: A

Question. The velocity of sound in air is not affected by change in
(a) moisture content of the air
(b) the temperature of air
(c) the atmospheric pressure
(d) the composition of air.
Answer: C

Question. The velocity of sound in any gas depends upon
(a) wavelength of sound only
(b) density and elasticity of gas
(c) intensity of sound waves only
(d) amplitude and frequency of sound.
Answer: B

Question. Transverse waves can propagate
(a) both in a gas and a metal
(b) in a gas but not in a metal
(c) not in a gas but in a metal
(d) neither in a gas nor in a metal.
Answer: C

Question. If the string of a pendulum were cut when the bob is at its central position, then bob would fall to the earth due to the absence of the
(a) force of buoyancy
(b) force of deformation
(c) force exerted by the string in the downward direction
(d) force exerted by the string in the upward direction.
Answer: D

Question. Though the forces are balanced at the mean position, even then the bob crosses over to the other extreme position after being released, because of
(a) inertia of the bob
(b) potential energy of the bob
(c) velocity of the bob
(d) none of these.
Answer: A

Question. If the mass of a pendulum is doubled, then time period
(a) becomes double
(b) becomes half
(c) velocity of the bob
(d) remains the same
Answer: D

Question. The time period T is found to depend upon L as
(a) \( T \propto L \)
(b) \( T \propto L^2 \)
(c) \( T^2 \propto L \)
(d) \( T \propto \frac{1}{\sqrt{L}} \)
Answer: C

Question. When the length of a pendulum is doubled and the mass of its bob is halved, then its time period would
(a) become double
(b) become half
(c) become \( \sqrt{2} \) times
(d) remain the same
Answer: C

Question. A pendulum having a period of oscillation of 2 seconds is taken on a planet where g is four times that on the earth. The period of the pendulum would be
(a) 2 s
(b) 1 s
(c) 4 s
(d) \( 2\sqrt{2} \) s
Answer: B

Question. It is possible to distinguish between transverse and longitudinal waves by studying the property of
(a) interference
(b) diffraction
(c) reflection
(d) polarization
Answer: D

Question. Mechanical waves having a frequency above the audible range, are called
(a) sonic
(b) ultrasonic’s
(c) infrasonics
(d) supersonics
Answer: B

Question. An anchored boat is rocked by waves whose crests are 100 m apart and whose velocity is 25 m/s. How often to the crests reach the boat?
(a) 0.35 s
(b) 4 s
(c) 75 s
(d) 25000 s
Answer: B

Question. The height of the crests of a wave is called as
(a) amplitude
(b) displacement
(c) frequency
(d) angular frequency
Answer: A

Question. The properties of ultrasound that make it useful are
(a) high power and high speed
(b) good directionally and high power
(c) high speed and frequency
(d) food directionally and ability to move around objects.
Answer: B

Question. If the density of air at a point through which a sound wave is passing is maximum at an instant, the pressure at that point will be
(a) minimum
(b) same as the density of air
(c) equal to the atmospheric pressure
(d) maximum.
Answer: D

Question. An object moving at a speed greater than that sound is said to be moving at
(a) ultrasonic speed
(b) sonic speed
(c) infrasonic speed
(d) supersonic speed.
Answer: D

Question. Sound travels at a speed of 332 m/s in air. This means
(a) the source of sound moves 332 m in one second
(b) the listener moves 332 m in one second
(c) air moves 332 m in one second
(d) the disturbance in air moves 332 m in one second
Answer: D

Question. Consider the following statements :
A. both sound wave and light wave are longitudinal
B. sound wave is longitudinal and light wave is transverse
C. sound wave is transverse and light wave is longitudinal
D. both sound wave and light wave are transverse
The correct statement is :
(a) A
(b) B
(c) C
(d) D
Answer: B

Question. A boat at anchor is rocked by waves whose consecutive crests are 0.1 km apart. The wave velocity of the moving crests is 72 km h^-1. what is the frequency of rocking of the boat?
(a) 0.4 Hz
(b) 0.2 Hz
(c) 0.6 Hz
(d) 0.5 Hz
Answer: B

Question. A wave pulse on a string moves a distance of 8 m in 0.04 s. What would be the wavelength of the wave on the same string if its frequency is 200 Hz?
(a) 0.4 m
(b) 0.5 m
(c) 0.8 m
(d) 0.10m
Answer: C

Question. The speed of light in water is \( 2.25 \times 10^8 \text{ m/s} \). If the speed of light in vacuum be \( 3 \times 10^8 \text{ m/s} \), calculate the refractive index of water.
(a) 0.33
(b) 1.33
(c) 1.04
(d) 2.43
Answer: B

Question. Non–mechanical waves can travel
(a) In vacuum as well as in a medium
(b) In vacuum but not in a medium
(c) In a medium but not in vacuum
(d) Neither in a medium nor in vacuum.
Answer: A

Question. The distance between a crest and the next through in a periodic waves is
(a) \( \lambda \)
(b) \( \lambda/2 \)
(c) \( \lambda/4 \)
(d) \( 2\lambda \).
Answer: B

Question. The distance between two successive crests or troughs is 1 m and the velocity of the waves is 320 ms^–1. What is the frequency?
(a) 340 Hz
(b) 400 Hz
(c) 320 Hz
(d) 420 Hz
Answer: C

Question. The wavelength of sound in air is 100 cm. Its frequency is:
(a) 33 c/s
(b) 330 c/s
(c) 100 c/s
(d) 3.3 c/s.
Answer: B

Question. Sound travels at a speed of 332 m/s in air. This means
(a) the source of sound moves 332 m in one second
(b) the listener moves 332 m in one second
(c) air moves 332 m in one second
(d) the disturbance in air moves 332 m in one second
Answer: D

Question. Non–mechanical waves can travel
(a) In vacuum as well as in a medium
(b) In vacuum but not in a medium
(c) In a medium but not in vacuum
(d) Neither in a medium nor in vacuum.
Answer: A

Question. The distance between two successive crests or troughs is 1 m and the velocity of the waves is 320 ms^–1. What is the frequency?
(a) 340 Hz
(b) 400 Hz
(c) 320 Hz
(d) 420 Hz.
Answer: C

Question. The wavelength of sound in air is 100 cm. Its frequency is:
(a) 33 c/s
(b) 330 c/s
(c) 100 c/s
(d) 3.3 c/s.
Answer: B

Question. A person has a hearing range from 20 Hz to 20 kHz. What are the typical wavelengths of sound waves in air corresponding to these two frequencies ? Take the speed of sound in air as 344 ms^–1.
(a) 16.2 m, 1.62 cm
(b) 16.2 m, 1.72 cm
(c) 16.7 m, 1.67 cm
(d) 17.2 m, 1.72 cm.
Answer: D

Question. Two particles are out of phase. What is the minimum path difference between them in terms of wavelength
(a) \( \lambda \)
(b) \( 2\lambda \)
(c) \( \frac{\lambda}{2} \)
(d) \( 4\lambda \)
Answer: C

Question. The time period T is found to depend upon L as
(a) \( T \propto L \)
(b) \( T \propto L^2 \)
(c) \( T^2 \propto L \)
(d) \( T \propto \frac{1}{\sqrt{L}} \).
Answer: C

Question. The graph between L and T² is
(a) [Straight line passing through the origin in a graph of \( T^2 \) vs \( L \)]
(b) [Curved line in a graph of \( T^2 \) vs \( L \)]
(c) [Negative slope line in a graph of \( T^2 \) vs \( L \)]
(d) [Decreasing curve line in a graph of \( T^2 \) vs \( L \)]
Answer: A

Question. The force which tries to bring the body back to its mean position is called
(a) deforming force
(b) restoring force
(c) gravitational force
(d) buoyant force.
Answer: B

Question. An observer standing at the sea–coast, observes 54 waves reaching the coast per minute. If the wavelength of wave is 10 m, then velocity of the wave will be
(a) 4.5 m/s
(b) 9 m/s
(c) 18 m/s
(d) 27 m/s.
Answer: B

Question. If a wave completes 20 vibrations in 2.5 s, then its frequency is
(a) 20 Hz
(b) 8 Hz
(c) 200 Hz
(d) 50 Hz
Answer: B

Question. Imagine a cannon being fired on the surface of the moon. Then the sound will
(a) be heard at the surface of the earth during all seasons
(b) not be heard at eh surface of the earth
(c) be heard at the surface of the earth during the rainy season
(d) not be heard on the earth or on the moon.
Answer: D

Question. In which of the following media will sound travel the fastest ?
(a) solid
(b) both solid and liquid
(c) liquid
(d) gas.
Answer: A

Question. Two waves travelling in a medium in the x-direction are represented by \( y_1 = A \sin(\alpha t - \beta x) \) and \( y_2 = A \cos(\beta x + \alpha t - \pi/4) \), where \( y_1 \) and \( y_2 \) are the displacements of the particles of the medium, t is time, and \( \alpha \) and \( \beta \) are constants. The two waves have different
(a) speeds
(b) directions of propagation
(c) wavelengths
(d) frequencies
Answer: B

Question. The equation \( y = a \cos^2(2\pi nt - 2\pi x / \lambda) \) represents a wave with
(a) amplitude a, frequency n and wavelength \( \lambda \)
(b) amplitude a, frequency 2n and wavelength \( 2\lambda \)
(c) amplitude a/2, frequency 2n and wavelength \( \lambda \)
(d) amplitude a/2, frequency 2n and wavelength \( \lambda/2 \)
Answer: D

Question. A wave travelling in a material medium is described by the equation y = a sin (kx - \( \omega \)t). The maximum particle velocity is
(a) A\( \omega \)
(b) \( \omega \)/k
(c) d\( \omega \)/dk
(d) x/t
Answer: A

Question. If two waves of the from y = a sin (\( \omega \)t – kx) and y = a cos (kx - \( \omega \)t) are superposed, the resultant wave will have amplitude
(a) 0
(b) a
(c) \( \sqrt{2} \) a
(d) 2a
Answer: C

Question. Wavelength of B.B.C. is 15 m, find the frequency of the waves broadcast by it if velocity of radio wave is \( 3 \times 10^8 \text{ m s}^{–1} \).
(a) 20 Mhz
(b) 30 MHz
(c) 200 Mhz
(d) 50 MHz.
Answer: A

Question. The wavelength of Monisha’s voice is 1 m and that of Mahesh’s voice is 2.5 m. Find the frequency of Monisha and Mahesh. Given the velocity of sound at room temperature is 350 m s^–1.
(a) 140 Hz
(b) 150 Hz
(c) 130 Hz
(d) 160 Hz.
Answer: A

Question. Find the length of a pendulum which will have the same time period on the moon as that of a pendulum of length 96 cm on the earth. The valve of acceleration due to gravity on the moon is one-sixth of that on earth.
(a) 16 cm
(b) 18 cm
(c) 26 cm
(d) 96 cm.
Answer: A

Question. A stone is dropped into a well 44.1 m deep. The sound of the splash is heard 3.2 s after the stone is dropped. Find the velocity of sound in air. (Take g = 9.8 m s^–2)
(a) 220.5
(b) 225.5
(c) 230.5
(d) 250.5.
Answer: A

Question. Calculate the length of simple pendulum whose time period is 1s.
(a) 0.148 m
(b) 0.248 m
(c) 0.348 m
(d) 02.48 m.
Answer: B

Question. Find the period of the pendulum whose length is 1 m.
(a) 2 s
(b) 1 s
(c) 6 s
(d) 10 s.
Answer: A

Question. Frequency of All India Radio Urdu Service is 710 kHz. What is its wavelength ? Given velocity of radio waves \( c = 3 \times 10^8 \text{ ms}^{–1} \).
(a) 422.5 m
(b) 423.5 m
(c) 425.5 m
(d) 435.5 m
Answer: A

Question. A source is producing 15 waves in 3 seconds. The distance between a crest and trough is 10 cm. Find the wavelength.
(a) 20 cm
(b) 30 cm
(c) 40 cm
(d) 50 cm.
Answer: A

Question. A body is vibrating 6,000 times in one minute. If the velocity of sound in air is 360 ms^-1, find (i) frequency of vibration in hertz; (ii) wavelength of wave produced.
(a) 2.6 m
(b) 3.6 m
(c) 2.5 m
(d) 5.5 m.
Answer: B

Short Answer Type :

Question. Is it possible to have longitudinal waves on a string ? A transverse wave on a steel rod ?
Answer: A string can only support transverse waves because it cannot provide the necessary restoring force for compression and rarefaction required for longitudinal waves. However, a steel rod can support both longitudinal waves (as it has bulk modulus) and transverse waves (as it has shear modulus).

Question. Can you hear your own words if you are standing in a perfect vacuum ? Can you hear your friend in the same conditions ?
Answer: No, sound requires a material medium for propagation. In a vacuum, there are no air molecules to carry sound waves, so you cannot hear your own words or your friend's words.

Question. A vertical rod is hit at one end. What kind of wave propagates in the rod if (a) the hit is made vertically (b) the hit is made horizontally ?
Answer: (a) If the hit is vertical (along the axis), longitudinal waves propagate. (b) If the hit is horizontal (perpendicular to the axis), transverse waves propagate.

Question. Two loudspeakers are arranged facing each other at some distance. Will a person standing behind one of the loudspeakers clearly hear the sound of the other loudspeaker or the clarity will be seriously damaged because of the ‘collision’ of the two sounds in between ?
Answer: The person will hear the sound clearly. According to the principle of superposition, waves can pass through each other without altering their individual characteristics or shape.

Question. Explain why :
(a) Velocity of sound is generally greater in solids than in gases.
(b) The velocity of sound in oxygen is lesser than in hydrogen.
Answer: (a) Velocity depends on the elasticity and density of the medium. Solids are far more elastic (stiff) than gases, which overcompensates for their higher density, leading to higher speeds. (b) In gases, velocity is inversely proportional to the square root of the molar mass (\( v \propto 1/\sqrt{M} \)). Since oxygen is denser/heavier than hydrogen, sound travels slower in it.

Question. The thunder of lightening is heard some moments after the flash is seen. Explain.
Answer: This is because light travels much faster (\( 3 \times 10^8 \text{ m/s} \)) than sound (approx. \( 340 \text{ m/s} \)). The light reaches the observer almost instantly, while the sound takes a significant amount of time to travel the same distance.

Question. How can one communicate other over the moon’s surface? Give reason.
Answer: Astronauts use radio waves (electromagnetic waves) to communicate because radio waves do not require a medium to travel, unlike sound waves which cannot travel on the moon due to the lack of an atmosphere.

Question. Will the time period of a pendulum vary from pole to equator of earth? Give reason.
Answer: Yes. The time period \( T = 2\pi\sqrt{L/g} \). Since the acceleration due to gravity \( g \) is greater at the poles than at the equator, the time period will be shorter at the poles and longer at the equator.

Question. Can you make a pendulum oscillating at the centre of the earth? Give reason.
Answer: No. At the center of the Earth, the effective acceleration due to gravity \( g \) is zero. Since \( T \propto 1/\sqrt{g} \), the time period would become infinite, meaning the pendulum would not oscillate.

Question. No sound energy from the sun reaches to earth. Can you come to the conclusion that the sun does not produce any sound energy?
Answer: No. The sun produces massive amounts of sound energy due to nuclear explosions, but this sound cannot reach Earth because space is a vacuum, and sound waves require a medium to propagate.

Question. Write two differences between sound wave and any electromagnetic wave.
Answer: 1. Sound waves are mechanical waves requiring a medium, while electromagnetic waves can travel through a vacuum. 2. Sound waves are longitudinal (in fluids), whereas electromagnetic waves are transverse.

Question. When vapour increases in atmosphere, what happens to the speed of sound? Give reason for your answer.
Answer: The speed of sound increases. Presence of water vapor reduces the effective density of air, and since \( v \propto 1/\sqrt{\text{density}} \), the speed increases.

Question. What is called reverberation? How is it reduced in a small room?
Answer: Reverberation is the persistence of sound due to multiple reflections even after the source has stopped. In small rooms, it is reduced using sound-absorbent materials like heavy curtains, carpets, or acoustic tiles.

Question. In a class room why don’t we receive any echo?
Answer: For a distinct echo to be heard, the distance between the source and reflecting surface must be at least 17.2 meters. Most classrooms are smaller than this, so the reflected sound reaches our ears too quickly to be distinguished from the original sound.

Question. What causes the change in velocity when sound wave changes medium while propagating?
Answer: The change in velocity is caused by the change in the physical properties of the medium, specifically its elasticity (modulus) and density.

Long Answer Type :

Question. What are longitudinal waves ? Give examples. How do such waves propagate ?
Answer: Longitudinal waves are waves in which the particles of the medium vibrate back and forth along the direction of wave propagation. Example: Sound waves in air. They propagate through a series of compressions (high-pressure regions where particles are close) and rarefactions (low-pressure regions where particles are spread out).

Question. Two children are at the opposite ends of an iron pipe. One strikes at end of the pipe with a stone. Find the ratio of time taken by sound waves in air and in iron rod reaching to the other child. Given velocity of sound in air and iron are 332 m s^–1 and 5,130 m s^–1 respectively.
Answer: Let the length of the pipe be \( d \).
Time in air \( t_{air} = d/332 \)
Time in iron \( t_{iron} = d/5130 \)
Ratio \( t_{air} / t_{iron} = 5130 / 332 \approx 15.45 : 1 \).

Question. A second’s pendulum (on earth) is taken to moon. What will be its time period there ?
Answer: A seconds pendulum has \( T_{earth} = 2 \text{ s} \). On the moon, \( g_{moon} = g_{earth}/6 \).
\( T_{moon} = T_{earth} \times \sqrt{g_{earth}/g_{moon}} = 2 \times \sqrt{6} \approx 4.89 \text{ s} \).

Question. Find the velocity of the wave as shown in figure [Graph showing displacement vs time in ms, with distance marker 2.5m between cycles].
Answer: From the graph, wavelength \( \lambda = 2.5 \text{ m} \) (distance between two consecutive crests). Time period \( T = 2 \text{ ms} = 0.002 \text{ s} \). Velocity \( v = \lambda/T = 2.5/0.002 = 1250 \text{ m/s} \).

Question. A man standing on a boat observes every after 5 second one crest is striking his boat. Two such crests are 1 m away from each other. In how much time 100 such crest will strike his boat. Find the velocity of the wave.
Answer: Time interval between crests \( T = 5 \text{ s} \). Distance between crests \( \lambda = 1 \text{ m} \). Velocity \( v = \lambda/T = 1/5 = 0.2 \text{ m/s} \). To hit 100 crests, there are 99 intervals, so total time = \( 99 \times 5 = 495 \text{ seconds} \).

Question. Describe an experiment to demonstrate that a wave does not carry any matter but carries energy?
Answer: Place a few cork pieces on the surface of calm water in a tub. Drop a stone at the center. Ripples (waves) will move outward. The cork pieces will only bob up and down at their positions, showing that water molecules (matter) do not travel with the wave, while the energy travels outward, causing the corks to move.

Question. In a certain planet gravitational acceleration is 3 times more than on the earth? Find the ratio of the time periods in the two planets.
Answer: Let \( g_{planet} = 4g_{earth} \) (3 times more means \( 1+3 \)).
\( T_{earth} / T_{planet} = \sqrt{g_{planet}/g_{earth}} = \sqrt{4/1} = 2 \).
Ratio is \( 2 : 1 \).

Question. A man standing between two hills makes sound loudly and receives two echoes after 1 sec and 1.2 sec. Find the distance between the two hills. [take v of sound = 330 m/s]
Answer: Distance to Hill 1: \( d_1 = (v \times t_1)/2 = (330 \times 1)/2 = 165 \text{ m} \).
Distance to Hill 2: \( d_2 = (v \times t_2)/2 = (330 \times 1.2)/2 = 198 \text{ m} \).
Total distance between hills = \( d_1 + d_2 = 165 + 198 = 363 \text{ m} \).

Question. A boy standing at a certain distance from a hill shouts loudly and starts running towards the hill at a speed of 5 m/s. He receives the echo after 5 second. Find the distance of the boy at initial position from the hill.
Answer: Let initial distance be \( D \). Distance traveled by boy in 5s = \( 5 \times 5 = 25 \text{ m} \).
Total distance traveled by sound = \( D + (D - 25) = 2D - 25 \).
Also, distance = speed \( \times \) time = \( 340 \times 5 = 1700 \text{ m} \) (assuming \( v = 340 \text{ m/s} \)).
\( 2D - 25 = 1700 \Rightarrow 2D = 1725 \Rightarrow D = 862.5 \text{ m} \).