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




Mechanical resonance:  Transfer of energy of vibration from one object to a second object having the same natural frequency.




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.



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




f1 = f2



λ1 >  λ2

V1 = f1. λ1

V2 = f2. λ2




V1 > V2




n:  Absolute index of refraction

θ1:  Angle in vacuum

θ2:  Angle in substance






Snellís Law:  n1.sin θ1 = n2.sin θ2








Snellís Law:  n1.sin θ1 = n2.sin θ2


n1 > n2

θ1 > θ2

θ2 = 90

θ1:  Critical angle

n1.sin θ1 = n2.sin 90






λ:  Wavelength (m)

w:  Width of the opening (m)


Higher the , higher the diffraction, or smaller the , smaller the diffraction





The two vibrating sources have same frequencies, amplitudes and in phase.


| Pn.S1 - Pn.S2 | = (n Ė 0.5). λ = Xn / L = sin θn


This formula is valid if Pn is far enough from S1 and S2 and the two vibrating sources have same frequencies, amplitudes and in phase.


Pn:  nth nodal point

n:  Nodal line number

θn:  Angle for the nth nodal line

S1:  First point of source of vibrating

S2:  Second point of source of vibrating

d:  Distance between the sources (m)

λ:  Wavelength (m)

L:  Distance from the midpoint of S1S2 to the point Pn

Xn:  Perpendicular distance from the right bisector of S1S2 to the point Pn