WAVE AND VIBRATIONS
Period: time for one cycle (s)
Frequency: Number of cycles in a unit of time (Hz)
Amplitude: Maximum distance of the vibrating object from its rest position (equilibrium position)
T: Period (s)
Dt: Time interval (s)
N: Number of cycles
f: frequency (Hz)
1 hertz (Hz) = 1
f . T = 1
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Mechanical resonance: Transfer of energy of vibration from one object to a second object having the same natural frequency.
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Wave: Disturbance that transfers energy through a medium by means of a series of vibrations. Energy transferred by means of waves, but the medium through which the wave is traveling does not move.
Transverse Waves: medium vibrates at right angles to the direction of travel of the wave.
Longitudinal Waves: Particles of the medium vibrate back and forth parallel to the direction in which the wave is traveling.
Wave in phase: If Objects have the same period and pass through the rest position at the same time, these objects will be called in phase.
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Speed of Waves:
Universal Wave Equation:
Dd = λ
Dt = T
λ: Wave length (m)
v = f. λ
Water wave from deep water to shallow water
Universal wave equation: v = f. λ
f: Frequency (1/s)
λ: Wavelength (m)
Deep Water 
Shallow Water 

f_{1} 
f_{2} 
f_{1} = f_{2} 
λ_{1} 
λ_{2} 
λ_{1} >_{ }λ_{2} 
V_{1} = f_{1}. λ_{1} 
V_{2} = f_{2}. λ_{2} 

V_{1} 
V_{2} 
V_{1 }>_{ }V_{2} 
n: Absolute index of refraction θ_{1}: Angle in vacuum θ_{2}: Angle in substance


Snell’s Law: n_{1}.sin θ_{1} = n_{2}.sin θ_{2}
_{ }
CRITICAL ANGLE
Snell’s Law: n_{1}.sin θ_{1} = n_{2}.sin θ_{2}
n_{1} > n_{2}
θ_{1} >_{ }θ_{2}
θ_{2} = 90
θ_{1: } Critical angle
n_{1}.sin θ_{1} = n_{2}.sin 90
_{ }
DIFFRACTION
λ: Wavelength (m)
w: Width of the opening (m)
Higher the , higher the diffraction, or smaller the , smaller the diffraction
INTERFERENCE OF WAVES IN TWO DIMENSIONS
The two vibrating sources have same frequencies, amplitudes and in phase.
 Pn.S_{1}  Pn.S_{2}  = (n – 0.5). λ = X_{n} / L = sin θ_{n}
This formula is valid if P_{n} is far enough from S_{1} and S_{2} and the two vibrating sources have same frequencies, amplitudes and in phase.
_{ }
P_{n}: nth nodal point
n: Nodal line number
θ_{n: } Angle for the nth nodal line
S_{1: } First point of source of vibrating
S_{2: } Second point of source of vibrating
d: Distance between the sources (m)
λ: Wavelength (m)
L: Distance from the midpoint of S_{1}S_{2 }to the point P_{n}
X_{n}: Perpendicular distance from the right bisector of S_{1}S_{2 }to the point P_{n}