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)

Snell’s Law:  n<sub>1</sub>.sin θ<sub>1</sub> = n<sub>2</sub>.sin θ<sub>2</sub>

CRITICAL ANGLE

Snell’s Law:  n<sub>1</sub>.sin θ<sub>1</sub> = n<sub>2</sub>.sin θ<sub>2</sub>

n<sub>1</sub> > n<sub>2</sub>

θ<sub>1</sub> > θ<sub>2</sub>

θ<sub>2</sub> = 90

θ<sub>1:</sub>  Critical angle

n<sub>1</sub>.sin θ<sub>1</sub> = n<sub>2</sub>.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<sub>1</sub> - Pn.S<sub>2</sub> | = (n – 0.5). λ = X<sub>n</sub> / L = sin θ<sub>n</sub>

This formula is valid if P<sub>n</sub> is far enough from S<sub>1</sub> and S<sub>2</sub> and the two vibrating sources have same frequencies, amplitudes and in phase.

P<sub>n</sub>:  nth nodal point

n:  Nodal line number

θ<sub>n:</sub>  Angle for the nth nodal line

S<sub>1:</sub>  First point of source of vibrating

S<sub>2:</sub>  Second point of source of vibrating

d:  Distance between the sources (m)

λ:  Wavelength (m)

L:  Distance from the midpoint of S<sub>1</sub>S<sub>2</sub> to the point P<sub>n</sub>

X<sub>n</sub>:  Perpendicular distance from the right bisector of S<sub>1</sub>S<sub>2</sub> to the point P<sub>n</sub>