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Class 9, Science, Chapter-11, Lecture-3, Characteristics of Waves (Notes)

WAVE CHARACTERISTICS:

The quantities required to describe a wave are called Wave Characteristics.

  • Wavelength: 
    The minimum separation at which the wave quantity at a given instant repeats its value regularly is called the 
    OR
    The distance between two nearest points in a wave which are in the same phase of vibration is called wavelength. 
    It is denoted by $\lambda$ (lambda). Its SI unit is metre (m).
  • Wave Number: 
    The reciprocal of wavelength is called wave number.
  • Amplitude: 
    The maximum change in the wave quantity from the state of zero disturbances is termed as amplitude. 
    OR
    The maximum displacement of a particle from the mean position is called amplitude. 
    It is denoted by $A$.
  • Time Period: 
    The time required to produce one complete wave is called time period of the wave. 
    It is denoted by $T$. Its SI unit is second (s)
  • Frequency: 
    The number of complete waves produced per unit time is called frequency of the wave. 
    It is denoted by $f$. Its SI unit is hertz (Hz)
  • Wave Speed: 
    The distance travelled by a wave per unit time is called wave speed.
    It is denoted by $v$. Its SI unit is metre per second (ms-1).

Relation Between Time Period and Frequency: 

Let ${\rm{T~s}}$ be the time period of a wave. 

$\therefore$ Number of waves produced in ${\rm{T~s}}$ $= 1$

$\therefore$ Number of waves produced in ${\rm{1~s}}$ $ = {1 \over {\rm{T}}}$

$ \Rightarrow $ frequency, ${{\rm{ ~ }}f{\rm{~ }} = {\rm{~ }}{1 \over {\rm{T}}}{\rm{~ }}}$

and time, ${{\rm{ T }}{\rm{~ }} = {\rm{~ }}{1 \over {\rm{~ }}f}{\rm{~ }}}$

Relation Between Velocity, Wavelength and Frequency: 

Let ${\rm{T~s}}$ be the time period of a wave and the wavelength be $ {\rm{\lambda ~m}}$. 
Let the wave speed be $v {\rm{ ~m}}{{\rm{s}}^{ - 1}}$ .

$\therefore$ Distance travelled by wave in ${\rm{T ~s}}$ $= {\rm{\lambda ~m}}$

$ \Rightarrow $ Distance travelled by wave in ${\rm{1 ~s}}$ $ = {{\rm{\lambda }} \over {\rm{T}}}{\rm{ ~m}}$

$ \Rightarrow $ Wave speed $v$ $~ = {{\rm{\lambda }} \over {\rm{T}}}{\rm{ ~m}}{{\rm{s}}^{ - 1}}$

$ \Rightarrow $ $v={{\rm{\lambda }} \over {\rm{T}}}{\rm{  =  \lambda }}\left( {{1 \over {\rm{T}}}} \right) = \lambda  f $ 

$ \Rightarrow $ $ v = f \lambda$ 

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