Galileo Galilei (15641642)
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.
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SHM concept Part 2
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Waves Concept part 2
Waves Concept part 3
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Subjective Question for waves
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Mechanics Index
Mechanics Index
Gravitation Concept
Conceptaul Question for Gravitation
Motion in a Plane
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objective Question for kinematics
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Conceptaul Question for Gravitation
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Conceptaul Question for Motion in a plane
objective Question for kinematics
Subjective Question for kinematics
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Conceptaul Question for relative velocty
Graphical Question for Motion in a Plane
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Conceptaul Question for Newton law of motion
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Momentum and Center of Mass
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Rotational Motion II
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Study Tips Part 2
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Conceptual Questions Part 2
Conceptual Questions Part 3
Conceptual Questions Part 4
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IITJEE Objective Questions Part 2
Thermal Expansion Problems
IITJEE Subjective Questions
Thermo Questions
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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)=[2A_{m}cos(υ/2)]sin(ωtkx+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
y_{i}(x,t)=A sin(ωtkx)then reflected wave at rigid boundary is
y_{r}(x,t)=A sin(ωt+kx+π)
=Asin(ωt+kx)
and for reflections at open boundary reflected wave is given by
y_{r}(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 (ωtkx) 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
f_{1}=v/2LSimilarly 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 f_{1} such that f_{n}=nf_{1}
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)=[2A_{m}cos(υ/2)]sin(ωtkx+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
y_{i}(x,t)=A sin(ωtkx)then reflected wave at rigid boundary is
y_{r}(x,t)=A sin(ωt+kx+π)
=Asin(ωt+kx)
and for reflections at open boundary reflected wave is given by
y_{r}(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 (ωtkx) 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
f_{1}=v/2LSimilarly 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 f_{1} such that f_{n}=nf_{1}
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