Waves Class 11 Notes Physics Chapter 15 - CBSE

Chapter : 15

What Are Waves ?

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    Transverse Waves

    These are the waves in which particles of the medium vibrate about their mean positions in a direction perpendicular to the directon of propogation of the disturbance.

    Longitudinal Waves

    These are the waves in which particles of the medium vibrate about their mean positions along the direction of propagation of the disturbance.

    Progressive Wave

    A wave that moves from one point of medium to another is called a progressive wave.

    Wave Velocity

    It is the distance travelled by a wave in one second.

    Relation Between Wave Velocity, Frequency And Wavelength

    v = nλ

    wave velocity = frequency × wavelength

    Velocity Of Transverse Waves

    $$\centerdot\space\text{In a solid}\space v =\sqrt{\frac{n}{\rho}}\\\centerdot\space\text{In a string}\space v = \sqrt{\frac{\text{T}}{m}}\\\text{where m is mass per unit length.}$$

    Velocity Of Longitudinal Waves

    • In a long root 

    $$v =\sqrt{\frac{n}{\rho}}\\\centerdot\space\text{In a liquid}\\\space v=\sqrt{\frac{K}{\rho}}\\\centerdot\space\text{In a gaseous medium}\\v = \sqrt{\frac{\text{K}}{\rho}}$$

    Factors Affecting Velocity Of Sound Through Gases

    • Effect of pressure – No effect
    • Effect of density

    $$v \propto\frac{1}{\sqrt{\rho}}$$

    • Effect of temperature,


    • Effect of humidity – Sound travels faster in moist air

    Wave Equation

    Wave propogating in +ve x-direction,

    $$\text{where\space k = 2}\pi/\lambda\\\centerdot\space\text{y = A sin}(wt - kx)\\\centerdot\space y = A \text{sin}\space 2\pi\bigg(\frac{t}{\text{T}}-\frac{x}{\lambda}\bigg)\\\centerdot\space\text{y = A sin}\frac{2\pi}{\text{T}}(vt - x)$$

    Principle Of Superposition Of Waves

    Resultant displacement

    y = y1 + y2 + y3 + ..........

    Stationary Wave

    When two progressive waves of equal amplitude and frequency, travelling in opposite direction along a straight line superimpose each other, the resultant wave does not travel in either direction and is called a stationary or standing wave.

    Modes Of Vibrations Of String

    •  For fundamental node,

    $$\lambda_{1} = 2\text{L}, v_{1} =\frac{v}{\lambda_{1}}\\=\frac{1}{\text{2L}}\sqrt{\frac{\text{T}}{\text{m}}} = v\space\text{(say)}$$

    • For second node,

    λ2 = L, v2 = 2n (second harmonic or first overtone)

    • For third node

    λ3 = 2L/3, v2 = 3v (third harmonic or second overtone)

    Laws Of Transverse Vibrations Of A Stretched String

    $$\centerdot\space v\propto\frac{1}{\text{L}}\\\centerdot\space v\propto\sqrt{T}\\\centerdot\space v\propto\frac{1}{\sqrt{m}}\\\text{Combing all,}\\v =\frac{1}{\text{2L}}\frac{\sqrt{\text{T}}}{m}\\=\frac{\text{L}}{\text{LD}}\sqrt{\frac{\text{T}}{\pi\rho}}$$

    Organ Pipe


    • For fundamental node

    $$\lambda_{1} = 4\text{L}, v_{1} =\frac{v}{\lambda_{1}} \\=\frac{1}{\text{4L}}\frac{\gamma \rho}{\rho} = v\text{(say)}$$

    • For second node,

    λ2 = - 4L/3, v2 = 3n (third harmonic or first overtone)

    ∴ v1 : v2: v3 : v4  = 1 : 3 : 5 : 7 :


    • For fundamental node

    $$\lambda_{1} = 2\text{L}, v_{1} =\frac{v}{2\text{L}} \\=\frac{1}{2\text{L}}\frac{\gamma\rho}{\rho} = v(\text{say})$$

    • For second node,

    λ2 = L, v2 = 2v

    (second harmonic or first ovetone)

    ∴ v1 : v2 : v3 : v4

    ...... = 1 : 2 : 3 : 4 : ....


    The periodic variations in the intensity of sound due to the superposition of two sound waves of slightly different frequencies are called beats. One rise and fall of intensity constitute one beat.