Mechanical waves  - Waves

Mechanical waves 

Lessons

Notes:

In this lesson, we will learn:

  • Wave properties
  • The relation between wave speed, wave-length, and the frequency.
  • Solving exercises relating variables.

Notes:

Periodic Waves
  • Pulse: Single disturbance of a medium
  • Periodic Waves: Continual disturbance of a medium.
    Particles in the medium move in a simple harmonic motion.

Mechanical Waves


    Crest: The top of the wave is called the crest; maximum displacement.

    (Note: in the case of longitudinal waves we use the term Compression, representing maximum pressure or maximum density)

    Trough: The bottom part of the wave is called the trough; minimum displacement.

    (Note: In the case of longitudinal waves the term Rarefaction is used, minimum pressure or minimum density)

Mechanical Waves

    Wavelength: The distance between two successive crests (troughs) called wavelength

Mechanical Waves

    Amplitude: The height of a crest or depth of a trough called amplitude.

    A high energy wave is characterized by a high?amplitude

    A low energy wave is characterized by a low?amplitude

Mechanical Waves

    Period: The time between two consecutive crests (troughs) called the period. The period is the time taken for one wavelength to pass by a point.

Mechanical Waves

    Frequency: Number of waves passing through a fixed point in ONE second.


    Table of terms and units of periodic motion

    \quadVariable\quad

    \quadSymbol \quad

    \quadStandard Units \quad

    Wavelength

    λ \lambda (Lambda)

    Meters (m)

    Amplitude

    A

    Meters (m)

    Period

    T

    Seconds(s)

    Frequency

    f

    Hz (hertz) =waves/seconds

    =1/seconds = (s-1 )

    Velocity: How fast the pulse is moving though a medium; the speed of the wave depends on the medium thought which it travels.

    Using the kinematic equation for constant velocity, the equation for speed (velocity) of the wave is given by:

    X=v.tv=Xt \triangle X = v.t \, \Rightarrow \enspace v = \frac{\triangle X} {t}

    Change in position (distance between two consecutive crests) of a wave is defines as its WAVELENGTH, therefore; 

    X=λ \triangle X = \lambda

    Time taken between two consecutive crests is defined as the PERIOD of the motion, therefore; t=T t=T

    v=Xt=λT(1)v=λT v = \frac{\triangle X} {t} = \frac{\lambda}{T} \qquad (1) \, v = \frac{\lambda}{T}

    Frequency is defined as number of waves per second, therefore; FREQUENCY is the reciprocal of the period,

    (2)f=1T (2) \, f = \frac{1}{T}


    From (1) & (2);

    (3)v=λT=λ(1T)=λf (3) \, v = \frac{\lambda}{T} = \lambda (\frac{1}{T}) = \lambda f \,
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    Mechanical Waves
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Mechanical waves 

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