Galileo Biograpgy

Galileo Galilei (1564-1642)


Galileo's experiments into gravity refuted Aristotle Galileo was a hugely influential Italian astronomer, physicist and philosopher.

Galileo Galilei was born on 15 February 1564 near Pisa, the son of a musician. He began to study medicine at the University of Pisa but changed to philosophy and mathematics. In 1589, he became professor of mathematics at Pisa. In 1592, he moved to become mathematics professor at the University of Padua, a position he held until 1610. During this time he worked on a variety of experiments, including the speed at which different objects fall, mechanics and pendulums.

In 1609, Galileo heard about the invention of the telescope in Holland. Without having seen an example, he constructed a superior version and made many astronomical discoveries. These included mountains and valleys on the surface of the moon, sunspots, the four largest moons of the planet Jupiter and the phases of the planet Venus. His work on astronomy made him famous and he was appointed court mathematician in Florence.

In 1614, Galileo was accused of heresy for his support of the Copernican theory that the sun was at the centre of the solar system. This was revolutionary at a time when most people believed the Earth was in this central position. In 1616, he was forbidden by the church from teaching or advocating these theories.

In 1632, he was again condemned for heresy after his book 'Dialogue Concerning the Two Chief World Systems' was published. This set out the arguments for and against the Copernican theory in the form of a discussion between two men. Galileo was summoned to appear before the Inquisition in Rome. He was convicted and sentenced to life imprisonment, later reduced to permanent house arrest at his villa in Arcetri, south of Florence. He was also forced to publicly withdraw his support for Copernican theory.

Although he was now going blind he continued to write. In 1638, his 'Discourses Concerning Two New Sciences' was published with Galileo's ideas on the laws of motion and the principles of mechanics. Galileo died in Arcetri on 8 January 1642.

Waves and Oscillation Index

Waves and Oscillation

SHM concept Part 1
SHM concept Part 2
Conceptaul Question for SHM
Subjective questions for SHM
objective Question for SHM
Waves Concept part 1
Waves Concept part 2
Waves Concept part 3
Conceptaul Question for waves
Objective Question for waves
Subjective Question for waves
IITJEE Test Series I

Mechanics Index

Mechanics Index

Gravitation Concept
Conceptaul Question for Gravitation
Motion in a Plane
Conceptaul Question for Motion in a plane
objective Question for kinematics
Subjective Question for kinematics
Relative Velocity Concept
Conceptaul Question for relative velocty
Graphical Question for Motion in a Plane
Newton's law of Motion Concept
Conceptaul Question for Newton law of motion
Uniform Cicular Motion-Friction-Frame of Refrence
Work And Energy
Momentum and Center of Mass
IIT JEE test series
Problem Solving tips for Mechanics
Challenging Problems Mechanics
15 min Test series
30 min Test series
PMT test series
Rotational Motion -I
Rotational Motion -II
Rotational Objective


Note: solution are available at the bottom of posts

Thermal Index

Thermodynamics Index.

Thermal Expansion
Study Tips Part 1
Study Tips Part 2
Thermo Quick Recap
Conceptual Questions Part 1
Conceptual Questions Part 2
Conceptual Questions Part 3
Conceptual Questions Part 4
IITJEE Objective Questions part 1
IITJEE Objective Questions Part 2
Thermal Expansion Problems
IITJEE Subjective Questions
Thermo Questions
Past Year AIEEE Thermo Questions
IITJEE test series 1
IITJEE test series 2



Note:Solutions are available at the bottom of each post

Waves Concept

PART2

Interference of waves:-
-From principle of superposition we know that overlaping waves algbrically add togather to produce a net wave without altering the way of each other or the individual waves.
-If two sinusoidal waves of the same amplitude and wavelength travell in the same direction they interfere to produce a resultant sinusoidal wave travelling in that direction.
-The resultant wave due to interference of two sinusoidal waves is given by the relation
y′(x,t)=[2Amcos(υ/2)]sin(ωt-kx+υ/2)where υ is the phase difference between two waves.
-If υ=0n then there would be no phase difference between the travelling waves and the interference would be fully constructive.
-If υ=π then waves would be out of phase and there interference would be distructive.

Reflection of waves:-
-When a apulse or travelling wave encounters any boundary it gets reflected.
-If the boundary is not completely rigid then then a part of wave gets reflected and rest of it's part gets transmitted or refracted.
-A travelling wave at a rigid boundary is reflected with a phase reversal but the reflection at open boundary takes place without phase change.
-if an incident wave is represented by
yi(x,t)=A sin(ωt-kx)then reflected wave at rigid boundary is
yr(x,t)=A sin(ωt+kx+π)
=-Asin(ωt+kx)
and for reflections at open boundary reflected wave is given by
yr(x,t)=Asin(ωt+kx)
Standing waves:-
-The interference of two identical waves moving in opposite directions produces standing waves.
-For a string with fixed ends standing wave is given by
y(x,t)=[2Acos(kx)]sin(ωt)above equation does not represent travelling wave since it does not have characterstic form involving (ωt-kx) or (ωt+kx) in the argument of trignometric function.
-In standing waves amplitude of waves is different at different points i.e., at nodes amplitude is zero and at antinodes amplitude is maximumwhich is equal to sum of amplitudes of constituting waves.
-At intermediate points amplitude of wave varies between these two limits of maxima and minima

Normal modes of stretched string:--Frequency of transverse motion of stretched string of length L fixed at both the ends is given by
f=nv/2L
where n=1,2,3,4,.......
-The set of frequencies given by above relation are called normal modes of oscillation of the system.
-The mode with n=1 is called the fundamental mode with frequancy
f1=v/2L-Similarly second harmonic is the oscillation mode with n=2 and so on.
-Thus the string has infinite number of possible frequency of viberation which are harmonics of fundamental frequency f1 such that fn=nf1

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