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## Tuesday, July 29, 2014

### CBSE IX Congruence of Triangle Solved Questions

CBSE Exam  Congruence of  Triangle Solved Questions
Q. 1. Prove that Sum of Two Sides of a triangle is greater than twice the length of median drawn to third side.
Given: Δ ABC in which AD is a median.
To prove: AB + AC > 2AD.
Construction: Produce AD to E, such that AD = DE. Join EC.
BD = BD             (D is the mid point of BC)
ADB = EDC       (Vertically opposite angles)
AB = ED               (CPCT)
In ΔAEC,
AC + ED > AE           (Sum of any two sides of a triangles is greater than the third side)

Q. 2. ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that BCD is a right angle.
In ΔABC,
AB = AC (Given)
⇒ ∠ACB = ∠ABC (Angles opposite to equal sides of a triangle are also equal)
⇒ ∠ADC = ∠ACD (Angles opposite to equal sides of a triangle are also equal)
In ΔBCD,
∠ABC + ∠BCD + ∠ADC = 180º (Angle sum property of a triangle)
⇒ ∠ACB + ∠ACB +∠ACD + ∠ACD = 180º
⇒ 2(∠ACB + ∠ACD) = 180º
⇒ 2(∠BCD) = 180º
⇒ ∠BCD = 90º

Q.3.Given: two triangles ABC and PQR in which AB=PQ, BC=QR , median AM =median PN prove that triangle ABC is congruent to triangle PQR.

In ∆ ABM  and ∆ PQN
AB   =  PQ                           ( Given )
AM  =  PN                           ( Given )
And  BM   =  QN   (  As M and N are the midpoint of sides BC and QR  respectively and given BC=  QR ) ∆ ABM
∆ PQN             ( By SSS rule )
SO,
ABM   =   PQN             ( by  CPCT )
Now  In ∆ ABC  and ∆ PQR
AB   =  PQ                           ( Given )
BC   =  QR                           ( Given )
And
ABC   =   PQR              ( As we proved )
∆ ABC    ∆ PQR            ( By SAS  rule )                                       ( Hence proved )

Q.4. The vertex angle of an isosceles triangle is twice the sum of its base angles. Find the measure of all the angles.
Let ABC be an isosceles ∆.Let the measure of each of the base angles = x
Let B = C = x
Now, vertex angle = A = 2x
Now,A + B + C = 180°   [angle sum property]
2x + x + x = 180°4x = 180x = 180/4=450
So, measure of each of the base angles = 45°
Now, measure of the vertex angle = 90°

Q. 5. Prove that the triangle formed by joining the midpoints of the sides of an equilateral triangle is also equilateral.
Let DEF be the midpoints of sides of a triangle ABC( with D on BC, E on AB and F on AC ).
Now, considering triangles AEF and ABC, angles
EAF = BAC and AE / AB = 1/2 and AF/AC = 1/2.
Hence, both triangles are similar by the SAS ( Side - Angle - Side ) criterion and correspondingly as AE/AB=AF/AC=EF/BC ( similar triangle properties ), EF =BC/2.
The cases DF=AC/2 and DE=AB/2 can be proved in the same way.
So, AB=BC=AC (from the given data)
2DF=2EF=2DE
DE=EF=DF
So triangle DEF is also Equilateral Triangle
The triangle formed by joining the mid-points of the equilateral triangle is also an equilateral triangle

Q. 6. In triangle PQR, PQ> PR. QS and RS are the bisectors of angle Q and angle R. Prove that SQ> SR
In PQR, we have,
PQ > PR               [given]
PRQ > PQR    [angle opposite to longer side of a  is greater]
12PRQ > 12PQR     ........(1)
Since, SR bisects R, thenSRQ = 1/2PRQ      ........(2)
Since SQ bisects P, thenSQR = 1/2PQR   .......(3)
Now, from (1), we have     1/2PRQ > 1/2PQR
⇒∠SRQ > SQR     [using (2) and (3)]
Now, in SQR, we have    SRQ > SQR       [proved above]
SQ > SR           [side opposite to greater angle of a  is longer

Q.7. In triangle ABC (A at the top) , D is any point on the side BC. Prove that AB+BC+CA 2AD
In triangle ABD,
AB+BD >AD (Sum of two sides of a triangle is greater than the third side) ... (1)
In triangle ACD,
AC+CD>AD (Sum of two sides of a triangle is greater than the third side)  ...(2)

Q.8. In triangle ABC, if AB is the greatest side, then prove that angle c is greater than 60 degrees
It is given that, AB is the longest side of the ∆ABC.
AB > BC   and  AB > AC.Now,    AB > BC⇒∠C > A    (angle opposite to longer side is greater)  ....(1)
Also,AB > AC⇒∠C > B    (angle opposite to longer side is greater)   ....(2)
we getC + C > A + B
2C > A + B2C + C > A + B + C3C > 180°⇒∠C > 60°

Q.9. AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see the given figure). Show that A > C and B > D.
Let us join AC.
In Δ ABC,
AB < BC (AB is the smallest side of quadrilateral ABCD)
∴ ∠2 < ∠1 (Angle opposite to the smaller side is smaller) ... (1)
∴ ∠4 < ∠3 (Angle opposite to the smaller side is smaller) ... (2)
On adding equations (1) and (2), we obtain
∠2 + ∠4 < ∠1 + ∠3
⇒ ∠C < ∠A
⇒ ∠A > ∠C

Let us join BD.
In ΔABD,
∴ ∠8 < ∠5 (Angle opposite to the smaller side is smaller) ... (3)
In ΔBDC,
BC < CD (CD is the largest side of quadrilateral ABCD)
∴ ∠7 < ∠6 (Angle opposite to the smaller side is smaller) ... (4)
On adding equations (3) and (4), we obtain
∠8 + ∠7 < ∠5 + ∠6
⇒ ∠D < ∠B            ⇒ ∠B > ∠D

Q.10.  If S. is any point on the side QR of triangle PQR, prove that PQ+QR+RP> 2PS
In   ΔPQS,
PQ + QS > PS   (i) ……………..(Sum of two sides of a triangle is greater than the third side)
In   ΔPSR,
PR + SR > PS  ……(ii)… Sum of two sides of a triangle is greater than the third side)
Adding (i) and (ii), we get
PQ + QS + PR + SR > 2PS
PQ + QR + PR > 2PS  (QS + SR = QR) Hence proved.

Q.11. Prove that the difference of any two sides of a triangle is less than the third side.
Construction: Take a Point D on AB such that AD = AC and join CD
Prove that : AB – AC < BC , AB – BC < AC and BC-AC <AB
Proof: In Δ ACD, Ext <4 > <2
but ,  AD = AC => <1 =  <2
So , < 4  > < 1 ----------------(i)
Now , In Δ BCD, ext <1 > <3 -------------(ii)
Then from (i)  and  (ii)
< 4  > <3      =>       BC > BD
But, BD = AB – AD and AD = AC         => BD = AB – AC
So, BC > AB – AC

Q.12. that Sum of any two sides of  triangle is greater than third side .
Solution:.
Construction: Extend BA to D Such that AD = AC
Proof : In Δ DACD,  DA=CA.
Therefore, ADC=ACD [ isosceles triangle have two equal angles]
Thus, BCD >BDC [by Euclid's fifth common notion.]
In  DCB
BCD >  BDC, So, BD>BC.
Thus,  BA+AC>BC.
A similar argument shows that AC+BC>BA and BA+BC>AC.

OR, Another way to prove
Draw a triangle,  ABC and line perpendicular to AC passing through vertex B.
Prove that BA + BC > AC

From the diagram, AM is the shortest distance from vertex A to BM. and CM is the shortest distance from vertex C to BM.
i.e. AM < BA and CM < BC
By adding these inequalities, we have
AM + CM < BA + BC
=> AC < BA + BC (
AM + CM = AC)
BA + BC > AC (Hence Proved)

Q.13. if one acute angle in a right angled triangle is double the other then prove that the hypotenuse is double the shortest side
Given: In Δ ABC , <B = 900 and <ACB = 2 <CAB
Prove that AC = 2BC
Construction: Produce CB to D such that BC  = BD Join  to AD
Proof :  In Δ ABD, and ABC
BD = BC ; AB = AB and <B = <B = 900
By SAS congruency ,    D  ABD ≅ ABC
<DAB = <BAC = X0
So, < DAC =  2X0
=> <ACB = <ACD
Now in Triangle Δ ADC, <DAC = <ACD= 2X0
=> AC = DC = 2BC Proved

Q. 14. Prove that in a triangle the side opposite to the largest angle is the longest.
Solution:
Given , in Δ ABC,  <ABC < <ACB
There is a triangle ABC, with angle ABC > ACB.
Assume line AB = AC
Then angle ABC = ACB, This is a contradiction
Assume line AB > AC
Then angle ABC < ACB, This also contradiction our hypothesis
So we are left with only one possibility ,AC> AB, which must be true
Hence proved:  AB < AC

Q. 15. Prove that in a triangle the angle opposite to the longer side is the longest.
Solution:
Given, in Δ ABC,  AC > AB.
Construction: Take a point D on AC such that AB = AD
So < ABD > <DCB (or ACB)
< ABC >  <ABD, so < ABC > <ACB

Q. 16.In a Δ ABC ,<B = 2<C. D is a point on BXC such that AD bisect < BAC and AB = CD. Prove that < BAC = 72 degree
In ΔABC, we have
∠B = 2∠C or, ∠B = 2y, where ∠C =  y
Let BP be the bisector of ∠ABC. Join PD.
In ΔBPC, we have
∠CBP = ∠BCP =  y  ⇒ BP = PC ... (1)
Now, in ΔABP and ΔDCP, we have
∠ABP = ∠DCP =  y
AB = DC  [Given]
and, BP = PC  [Using (1)]
So, by SAS congruence criterion, we have
Δ ABP  Δ DCP
<BAP = < CPD and AP = DP
<CDP = 2x  then <ADP = < DAP = x    [<A = 2x]
In ΔABD, we have
∠ADC = ∠ABD + BAD ⇒  x  + 2x   = 2y  +  x  ⇒  x  =  y
In ΔABC, we have
∠A + ∠B + ∠C = 180°
⇒ 2x  + 2y  +  y  = 180°
⇒ 5x  = 180°
⇒  x  = 36°
Hence, ∠BAC = 2x  = 72°

You may also use this way:

Q.17,  If o is any point in the interior of triangle ABC .Prove that
(a)  AB + AC > OB + OC
(b) AB + BC + CA > OA + OB + OC
(c )OA +OB+OC>1/2(AB+BC+CA)
Construction: Produce BO to meet AC at D
In D ABD, AB + AD > BD => AB + AD > OB + OD   ------(i)
In D OCD, OD + DC > OC    ------(ii)
Adding (i) and (ii) we get,
AB + AD + OD + DC  > OB + OD + OC
=> AB + AC > OB + OC    --------- (iii)                   Hence prove (a)
Similarly we get ,
BC + BA > OA + OC                ---------(iv)
and , CA + CB > OA + OB       ---------(v)
2(AB + BC + CA) > 2(OA + OB + OC)
AB + BC + CA > OA + OB + OC                       Hence prove (b)
In D  OAB , D OBC and D OCA
[OA + OB > AB ] + [OB + OC>BC] + [ OC + AO > AC]
2[OA + OB + OC]  > AB + BC + CA
[OA + OB + OC]  > ½ [AB + BC + CA]
Hence prove (c)
Check more stuff on CBSE IX  Congruence of  Triangle

## Saturday, July 26, 2014

### IX CBSE - Formative Assessment-II IX Biology - Improvement in Food Resources

IX CBSE - Formative Assessment-II [SET-1]

Q.1. What are green revolution and white revolution?

Q.2. What nutrients do the following provide:

(i) Pea (ii) Linseed (iii) Vegetables (iv) pigeon pea

(v) Wheat (vi) Castor (vii) Spices (viii) fruits.

Q.3. Differentiate between Kharif and Rabi crops.

Q.4. What is interspecific hybridization?

Q.5. How does change in maturity duration of crop help the framers?

Q.6. Categorize the following as macronutrients and micronutrients:

(i) Calcium (ii) Molybdenum (iii) Phosphorus

(iv) Iron (v) Boron (vi) Magnesium.

Q.7. What is organic farming?

Q.8. What is vermicomposting?

Q.9. Differentiate between mixed and inter cropping.

Q10. What are river lift systems?

Q.11. Why are weeds considered as unwanted plants in cultivated lands?

Q.12. In what three ways do the pests attack plants?

IX CBSE - Formative Assessment-II [SET-2]

Q.1. What qualities are expected in a cross-breed variety of fowl?

Q.2. Differentiate between capture fishing and culture fishing.

Q.3. What is composite fish culture system?

Q.4. Which Italian bee variety is used in India to yield honey?

Q.5. What is the use of Satellites and echo sounders in marine fishery?

Q.6. _________, ________ and _______ are some biotic factors responsible for storage losses.

Q.7. _________ is the scientific management of animal livestock.

Q.8. Milk-producing animals are called ________________________

Q.9. What qualities of Brown Swiss and Sahiwal are considered to use them for crossbreeding?

=============================================

Value Based Questions

Q.10. Seema and her mother went to a party and were appalled by the amount of food wasted by the
people. Sema‟s mother told her to take only that much food in her plate that she could eat. After the party
got over, Seema‟s mother asked the host to call the local NGO that would distribute the unused food to
poor people.

(i) State two methods to increase the production of food crops.

(ii) Why is storage of grains considered a very important aspect of agriculture?

(iii) What values are shown by Seema‟s mother?

IX Biology : Improvement in Food Resources

CBSE solved ,unsolved test papers,Notes, Assignments and Guess Papers  : First Term:  Improvement in
Food Resources. Plant and animal breeding and selection for quality improvement and management; use of fertilizers, manures; protection from pests and diseases; organic farming.

IX- Improvement in Food Res Solved Questions
IX- Imp. Food Resources:Revision assignment
IX- Food Resources Quick revision notes by KV

## Wednesday, July 23, 2014

### 8th/9th Chapter-Sound Physics CBSE Solved paper

IX Class Question solution for Physics Chapter Sound
1. How sound is produced?
Answer:   Sound is produced by the vibration of vibrating object.
2. What do you understand by a ‘wave’?
Answer:  A periodic disturbance created in material medium that transfer sound and light energy is called wave.
3. Write three differences between sound and light waves.
Answer:   sound wave is Mechanical wave that require material medium for propagation where as light waves are electromagnetic wave that can travel in vacuum.
4. What do you understand by “sound energy cannot be produced”?
Answer: Sound energy cannot be produced on its own. Some mechanical energy is required to make an object vibrate. It is the mechanical energy of the vibrating object which travels through a medium and ultimately reaches the ear.
5. What is the name of the wave that can travel through vacuum?
6. Explain by some experiment that sound waves require medium for their propagation.
Answer: An electric bell is suspended inside an airtight glass bell jar connected to a vacuum pump. As the electric bell circuit is completed, the sound is heard. Now if the air is slowly removed from the bell jar by using a vacuum pump, the intensity of sound goes on decreasing and finally no sound is heard when all the air is drawn out. We would be seeing the hammer striking the gong repeatedly. This clearly proves that sound requires a material for its propagation.
7. How sound waves travel through some medium?
Answer:   Sound waves work travel through some medium by passing vibrations from molecule to molecule. If there is no medium, then there no molecules to pass vibrations.
8. Why sound waves do not propagate through vacuum?
Answer:   If there is no medium, then there no molecules to pass vibrations.
9. What are the transverse waves? Give two examples.
A wave in which the particles of the medium vibrate at right angles to the direction, in which the wave is moving, is called transverse wave. Example: Light waves.
10. What are longitudinal waves? Give two examples.
A wave in which the particles of the medium vibrate back and forth in the same direction in which the wave is moving is called longitudinal wave. Example: sound waves.
11. Give two points of difference between longitudinal and transverse waves.
Answer:   Differences between the transverse wave and longitudinal wave:-
Transverse wave :-
(1)A transverse wave is a wave in which variation of the amplitude of a wave is perpendicular to the direction of propagation of wave.
(2) Light wave, wave in string, wave developed in water etc.
(3)In light wave electric and magnetic field oscillates normally to the direction of motion of the wave.
(4) It may propagate in the vacuum.
Longitudinal wave :-
(1)A longitudinal wave is a wave in which variation of the amplitude of wave is in the direction of the propagation of wave.
(2)sound wave, oscillation in the spring.
(3) In spring wave elongation or compression occurs along the direction of motion of the wave.
(4) It can not propagate in the vacuum.
12. How will you prove that the sound waves exhibit longitudinal behaviour?
Answer:   Take a tuning fork and a hard pad. Allow the tuning fork to strike the pad which makes the prongs to vibrate. When it starts vibrating, the inward and outward movements takes place in prong which causes the movement of inward and outward towards the mean position.The tuning fork is given as,

The vibaration of the tuning fork produces the compressions and refractions of the sound in the air,

When the tuning fork vibrates in air, they force the particles of the air to vibrate back and forth by a small distance. While vibrating, when the prong moves to the right side, it sends out a compression and when the prong moves to the left, it produces a rarefraction in air.
The longitudinal waves in series produce compressions and rarefractions in air from the tuning fork. These compressions and rarefractions of sound waves is formed by the vibrating particles causing vibration in the ears, the eardrum vibrates for reproduction of sound.
13. What are rarefaction and compression in case of sound waves?
Answer:   Compressions: Areas in the wave where the air molecules are pushed close together and so at a slightly higher pressure.
Rarefaction: Areas in the wave where the air molecules are further apart and so at a slightly lower pressure.
14. Distinguish between crests and troughs.
Answer:   The highest point of a wave is known as its crest while the trough is the lowest point of the wave. Wavelength is the horizontal distance between successive crests or troughs.
15. Write the SI unit of velocity of a wave.
16. What are the factors that describe the sound wave and define them?
17 .Why is a thundering sound heard later than lightening?
Answer:   This because the speed of sond is much lesser than that of light.
18. Sound travels with different speeds in different media. Comment.
Answer:   Sound waves need to travel through a medium such as a solid, liquid, or gas. The sound waves move through each of these mediums by vibrating the molecules in the matter. The molecules in solids are packed very tightly. Liquids are not packed as tightly as solids. And gases are very loosely packed. The spacing of the molecules enables sound to travel much faster through a solid than a gas. Sound travels about four times faster and farther in water than it does in air. This is why whales can communicate over huge distances in the oceans. Sound waves travel about thirteen times faster in wood than air. They also travel faster on hotter days as the molecules bump into each other more often than when it is cold.
19. How far are a compression and its nearest rarefaction in a longitudinal wave?
20. Define sound ranging.
Answer:   The method of  the determination of the location of a source of sound waves by measuring the time lapse between their transmission and their reception
21. What is the frequency range of sound for human beings?
22. What are the ultrasonic and supersonic waves?
Answer:   Ultrasonic waves refers to sound of  frequencies greater than those that can be heard (usually frequencies above 20 kHz).
Supersonic refers to sound of velocities faster than the speed of sound (in the medium under consideration).
23. What type of waves are produced by animals like bats and dolphins?
24. Explain two applications of ultra sound waves?
Answer:   Ultrasound is a wave with frequency greater than the upper limit of human hearing. These waves travel along well -defined paths and can even penetrate obstacles.
Some important applications of ultrasound are:
a. It is used for medical diagnosis and therapy and also to clean parts located in hard-to-reach places, for example, spiral tube, electronic components etc.
b. Ultrasound is used to detect cracks and flaws in metal blocks. Such as aeroplane wings can be checked for cracks that would be invisible on the surface.
c. Its use in scanning goes far beyond pregnancies. Many other parts of the body are analysed using it (bladder gallstones, the heart, etc.)
d. Detection of developmental/ structural abnormalities in the fetus. Evaluation of the heart and diagnosis of cardiac problems. This technique is called ‘Echocardiography’.
25. Ultrasound is also used to break small ‘stones’ formed in the kidneys into fine grains.25. Explain how ultrasound waves are used to detect a flaw in an object?
Answer:   The ultrasound waves are allowed to pass through metal block to which are fitted detectors to detect the waves. Ultrasounds can be used to detect minor cracks or flaws in metal block. For this, ultrasonic waves are allowed to pass through metal blocks and detectors are used to detect the transmitted waves. If there is a crack in metal block, these waves get reflected back, thus indicating the presence of defects or flaws like cracks in the metal block. 26. Which sound wave is used in ECG (echocardiography)?
27. Give the full form of SONAR.
28. Name the technique used to measure the depth of a sea.
29. How will you determine the depth of a sea using SONAR?
Answer:   ONAR is an acronym for Sound Navigation And Ranging. It is an acoustic device used to measure the depth, direction, and speed of under-water objects such as submarines and ship wrecks with the help of ultrasounds. It is also used to measure the depth of seas and oceans.

A beam of ultrasonic sound is produced and transmitted by the transducer (it is a device that produces ultrasonic sound) of the SONAR, which travels through sea water. The echo produced by the reflection of this ultrasonic sound is detected and recorded by the detector, which is converted into electrical signals. The distance ( d ) of the under-water object is calculated from the time ( t ) taken by the echo to return with speed ( v ) is given by 2d = v × t . This method of measuring distance is also known as ‘ echo-ranging’.
30. How do the bats fly in dark?
Answer:   Bats fly in the darkness of night without colliding with other objects by this method called echolocation. Bats emit high-frequency ultrasonic squeaks while flying & listen to the echoes produced by the reflection of their squeaks from the objects ( or obstacles ) in their path. From the time taken by the echo to be heard, bats can judge the distance of the object (or obstacle) in their path and  hence avoid it by changing the direction.
Notes: Bats search their prey at night by this method only.This happens as follows : Bats emit high-frequency ultrasonic squeaks while flying & listen to the echoes produced by the reflection of their squeaks from the prey like a flying insect.From the time taken by the echo to be heard, bats can judge the distance of the insect & hence can catch it.
31. How RADAR is different from SONAR?
Answer:   SONAR (Sound Navigation and Ranging) uses sound wave which is mechanical energy  to "look" through water or other media, and RADAR (Radio Direction and Ranging) uses electromagnetic radiation(radio waves) to "look" through the air or other media.
RADAR signals are mostly used for ground or atmospheric observations whereas SONAR signals are ideal for navigation and measurement under water.
32. Explain the function of ear by explaining its each part?
Answer:   The outer ear is called ‘pinna’ collects the sound from the surroundings. 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 a compression of the medium reaches the eardrum the pressure on the outside of the membrane increases and forces the eardrum inward. Similarly, the eardrum moves outward when a rarefaction reaches it. In this way the eardrum vibrates. The vibrations are amplified several times by three bones (the hammer, anvil and stirrup) in the middle ear. The middle ear transmits the amplified pressure variations received from the sound wave to the 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.
Note: The stirrup bone of the middle ear is the smallest bone in human body.
33. Distinguish between loudness and intensity of sound.
Answer:    Intensity depends on the energy per unit area of the wave and it is independent of the response of the ear, but the loudness depends on energy as well as on the response of the ear.
34. Why are ceilings of concert halls curved?
Answer:    The ceilings of concert hall are curved, so that sound after reflection from it reaches all the corners of the hall, and hence, is audible to everyone in the hall.
35. The frequency of a source of sound is 100 Hz. How many times does it vibrate in a minute?
Answer:    Number of vibrations produced in 1 second = 100
Number of vibrations produced in 1 minute (60 s) = 100 × 60 = 6000.
36. Give two practical applications of the reflection of sound waves. [2010]
Answer:    (i) In stethoscope the sound of patient’s heartbeat reaches the doctor’s ears by multiple reflections in the tubes.
(ii) Megaphones are designed to send sound waves in particular direction are based on the  reflection of sound.
37. Why are longitudinal waves called pressure waves?
Answer:   Sound waves travels in the form of compression and rarefactions, which involve change in pressure, and volume of the air. Thus they are called pressure waves.
38. What are harmonics?
Answer:    harmonics are notes of frequency which integral multiple of the fundamental frequency produced by a device. For e.g. third harmonic is 3 times the fundamental frequency.
39.   What are fundamental note and overtones?
Answer:    When a sound is produced, there are tones of different frequencies. The tone of lowest frequency is called fundamental note and the tones of higher frequency are called overtones.
Q.40   Sound travels faster on a rainy day than on a dry day. Why?
Answer:    Sound travels faster on rainy day because the velocity of sound increases with increase in humidity. On rainy day humidity is more thus velocity of sound is aso more.
Q.41   Why are the window panes of houses sometimes cracked when a bomb explodes even at large distance?
Answer:    The windows breaks because of the generation of shock waves in the explosion.
Q42   If the tension in the wire is increased four times how will the velocity of wave in a string varies?

Answer:    velocity of the wave in string is directly proportional to the square root of the tension thus if tension is increased 4 times the velocity will be doubled.

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