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Waves class 11 Notes Physics

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CBSE Class 11 PHYSICS
Revision Notes
CHAPTER 15
WAVES

Transverse and longitudinal waves
Displacement relation in a progressive wave
The speed of a travelling wave
The principle of superposition of waves
Reflection of waves, Beats, Doppler effect

Angular wave number: It is phase change per unit distance.

i.e. $k = \frac{2}{\pi }$ ; S.I unit of k is radian per meter.

Relation between velocity, frequency and wavelength is given as :-

Velocity of Transverse wave:-

In solid molecules having modulus of rigidity ‘n’ ’ and density ‘ρ’ is

$V = \sqrt {\frac{n}{p}}$

In string for mass per unit length ’m’ and tension ‘T’ is $V = \sqrt {\frac{T}{m}}$

Velocity of longitudinal wave:-

(i) in solid $V = \sqrt {\frac{Y}{p}}$ , Y= young’s modulus
(ii) in liquid $V = \sqrt {\frac{K}{P}}$ , K=bulk modulus
(iii) in gases , K= bulk modulus

According to Newton’s formula: When sound travels in gas then changes take in the medium are isothermal in nature.

$V = \sqrt {\frac{P}{P}}$

According to Laplace: When sound travels in gas then changes take place in medium are adiabatic in nature.

$V = \sqrt {\frac{{P\gamma }}{p}} \;\;where\;\;\gamma = \frac{{Cp}}{{Cv}}$

Factors effecting velocity of sound :-

(i) Pressure – No effect
(ii) Density $- v\alpha \frac{1}{{\sqrt p }}\,\,or\;\frac{{V1}}{{V2}} = \sqrt {\frac{{{\rho ^1}}}{{{\rho ^2}}}}$
Temp- $V\alpha \sqrt T \;\;\;or\;\frac{{V1}}{{V2}} = \sqrt {\frac{{T1}}{{T2}}}$
(iii) Effect of humidity:– sound travels faster in moist air
(iv) Effect of wind –velocity of sound increasing along the direction

Wave equation if wave is travelling along +ve x-axis

Y=A sin (ax – kx), Where, $K = \frac{{2\pi }}{\gamma }$
${\text{Y}} = {\text{A sin 2}}\pi {\text{(}}\frac{t}{T}\; - \;\frac{x}{\lambda })$
${\text{Y}} = {\text{A sin }}\frac{{2\pi }}{\gamma }(vt - x)$

If wave is travelling along –ve x- axis

${\text{Y}} = {\text{A sin }}\left( {{\text{ax + kx}}} \right),{\text{ Where}},{\text{ K}} = \frac{{2\pi }}{\gamma }$
${\text{Y}} = {\text{A sin 2}}\pi {\text{(}}\frac{t}{T}\; - \;\frac{x}{\lambda })$
${\text{Y}} = {\text{A sin }}\frac{{2\pi }}{\gamma }(vt + x)$

Phase and phase difference

Phase is the argument of the sine or cosine function representing the wave.

$\phi = 2\pi (\frac{t}{T} - \frac{x}{\lambda })$ Relation between phase difference ( $(\Delta \phi )$ and time interval is $\Delta \phi = \frac{{2\pi }}{T}\Delta t$

Relation between phase difference $(\Delta p)$ and path difference $(\Delta x)$ is $\Delta \phi = \frac{{2\pi }}{\lambda }\Delta x$

Equation of stationary wave:-
$\;{Y_1} = a\;\sin \,2\pi \left( {\frac{t}{T} - \frac{x}{\lambda }} \right)\left( {{\text{ incidnet wave}}} \right)$
$\;{Y_1} = \pm \;a\;\sin \,2\pi \left( {\frac{t}{T} + \frac{x}{\lambda }} \right)\left( {{\text{reflected wave}}} \right)$

(1) Stationary wave formed
$Y = {Y_1} + {Y_2} = \pm 2a\;\cos \frac{{2\pi x}}{\lambda }\;\sin \frac{{2\pi l}}{T}$

(2) For (+ve) sign antinodes are at x= 0, $\frac{\lambda }{2},\;\lambda ,\;\frac{{3\lambda }}{2}$

(3) For (-ve) sign antinodes are at x= $\frac{\lambda }{4},\;\;\frac{{3\lambda }}{2},\frac{{5\lambda }}{4}.....$
Nodes at x= 0, $\frac{\lambda }{2},\;\lambda ,\;\frac{{3\lambda }}{2}$

(4) Distance between two successive nodes or antinodes are $\frac{\lambda }{2}$ and that between nodes and nearest antinodes is $\frac{\lambda }{4}$

(5) Nodes- point of zero displacement-
Antinodes- point of maximum displacement-

A = Antinodes
Mode of vibration of strings:-

$v = \frac{p}{{2L}}\sqrt {\frac{T}{m}\;} \;where,\;T = Tension$

M= mass per unit length
V= frequency, V=velocity of second , P=1, 2, 3, …..

b) When stretched string vibrates in P loops $\nu {\rm P} = \frac{{\rm P}}{{2L}}\sqrt {\frac{T}{m}} \; = \;{\rm P}\nu$
c) For string of diameter D and density ρ $\nu = \frac{1}{{LD}}\sqrt {\frac{T}{{\pi {\rm P}}}} \;$
d) Law of length $\nu x\alpha \frac{1}{L},\nu L$ = constant

Waves class 11 Notes

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CBSE Class-11 Revision Notes and Key Points

Waves class 11 Notes Physics. CBSE quick revision note for class-11 Physics, Chemistry, Maths, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

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Waves class 11 Notes Physics

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Waves class 11 Notes Physics

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Waves class 11 Notes

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