NEET Exam  >  NEET Notes  >  NCERT Exemplar & Revision Notes for NEET  >  Revision Notes: Waves & Sound Waves

Waves Class 11 Notes Physics Chapter 14

Waves:- 

  • Wave motion:- Wave motionis the disturbance, set up in the medium, due to the repeated periodic motion of the particles of the medium and travels from the particle to particle, the particles themselves keep vibrating about their mean positions.
  • Wave Equation:- d2y/dt2 = v2 (d2y/dx2
  • Transverse wave motion:-It is the type of wave motion in which the particles of the medium are vibrating in a direction at right angles to the direction of propagation of wave.
    (a) Velocity of transverse wave,Vt = √T/m = √T/πr2ρ
    (b) Vibrations of the particles of medium are normal to the direction of wave propagation.
    Waves Class 11 Notes Physics Chapter 14
  • Longitudinal wave motion:-It is the type of wave motion in which the particles of the medium vibrate in the direction of propagation of wave.
    Waves Class 11 Notes Physics Chapter 14(a) Velocity of longitudinal wave, V= √E/ρ
    (b) Vibrations of the particles are parallel to the direction of wave propagation. 
  • Terms related to wave motion:-
    (a) Wave length(λ):- 
    (i) It is defined as the distance travelled by a wave during the time particle executing SHM completes one vibration.
    (ii) It is the distance between two consecutive particles executing SHM in same phase.
    (iii) It is the distance between two consecutive crests or troughs.
    (b) Wave number (n):- Wave-number of a wave is defined as the reciprocal of wavelength of weave.
    n = 1/λ
    Unit of weave number is meter.
    Waves Class 11 Notes Physics Chapter 14(c) Velocity of wave:- It is the distance (λ) travelled by the wave during the time (T), a particle completes one vibration.
    velocity of wave = (frequency) (wavelength)
    v=fλ
    (d) Phase:- Phase of a particle is its state which expresses its position and direction of motion.
    (e) Phase difference: Phase difference, between two particles, is the difference between their instantaneous phases.
  • Relation between phase difference (?) and path difference (λ):-
    ? = (2π/λ)×(path difference)
  • Simple Harmonic Motion:-A wave which originates from a source, undergoing simple harmonic motion, is called a simple harmonic wave.
    Equation:-y=rsinωt
    = r sin2πft
    = rsin2π(v/λ)t
    = r sin2πx/λ
    Waves Class 11 Notes Physics Chapter 14
  • Equation of progressive wave:- A relation between the instantaneous displacement of a particle executing SHM and time is called equation of progressive wave.
    Waves Class 11 Notes Physics Chapter 14
    y = r sin2π (ωt± ?)
    y = r sin [(ωt± (2π/λ)x]
    y = r sin (ωt± kx)
    y = r sin 2π (t/T ± x/λ)
    y = r sin 2π/λ (vt± x)
  • Angular wave number (k): k = 2π/λ
  • Relation between particle velocity (V) and wave velocity (v):-
    V = (2πr/λ) vcos[(2π/λ)(vt±x)]
    Vmax = (2πr/λ) v
  • Energy transmission in a progressive wave:-E = ½ mω2r2
  • Energy per unit volume:- E = ½ ρr2ω2  Here ρ is the density of medium.
  • Intensity of a wave:-
    I = 2π2ρvf2r2
    Intensity of a wave varies directly as the square of its amplitude.
    So, I∝r2
  • Velocity of transverse wave in stretched string:-v = √(T/m), Here,T is the tension in the string.
  • Interference:- Interference is the phenomenon by virtue of which there is a modification in the distribution of energy due to super position of two or more waves.
    y= a1sinωt, y2 = a2sin(ωt+?)
    y = y1+y2 
    Amplitude, A = √[a12+a22+2 a1 a2cos?])
    Intensity, I = kA2 and I = I1+I2+2(√ I1I2) cos?
    Here, I1 = ka12 and I2 = ka22
    Angle, θ = tan-1[a2sin?/(a1+a2cos?)]
    Waves Class 11 Notes Physics Chapter 14
  • Constructive interference:-
    Phase difference, ? = 2nπ,  n = 0,1,2,3…
    A = a1+a2
    Imax = [√I1+√I2]2
    Path difference, x = 2n(λ/2)
    Waves Class 11 Notes Physics Chapter 14
  • Destructive interference:-
    Phase difference, ? = (2n+1)π,  n = 0,1,2,3…
    A = 2acos?/2
    I = 4a2k cos2?/2
    Imax = 4a2k
    Imin = 0
    Path difference, x = (2n+1)(λ/2)
  • Condition for interference:-
    (a) The two sources must emit continuous waves having same frequency and wavelength.
    (b) The amplitudes of two waves must either be equal or nearly equal.
    (c) The two sources should be situated close to each other.
    (d) The two sources should be coherent one.
  • Stationary Wave:-
    Wave equation, y = 2acos (2π/λ) x sin (2π/λ) vt
    Amplitude, A = 2acos(2π/λ) x
    Condition for maxima (anti-nodes), x = k(λ/2)
    Condition for minima (nodes), x = (2k+1)(λ/4)
  • Frequency of transverse vibrations in stretched string:-
    f=(1/2l) √(T/m), Here l is the length, T is the tension and m is the mass.
    f=(1/lD) √(T/πρ), Here l is the length, T is the tension, D is the diameter and ρ is the density.
  • Harmonics in stretched strings:-
    (a) First harmonic (fundamental frequency),  f0=(1/2l) √(T/m)
    (b) Second harmonic (first overtone), f1 = 2f0=(2/2l) √(T/m)
    (c) Third harmonic (second overtone), f2 = 3f0=(3/2l) √(T/m)
    (d) pth harmonic (p-1 overtone),  fp-1 = pf0=(p/2l) √(T/m)
    Here, p=1,2,3…
  • Frequency of tuning fork:-
    f∝(t/l )√(E/ρ)
    Here, t is the thickness, l is the length, E is the elastic constant and ρ is the density.
  • Phenomenon of Beats:- Periodicvariations of amplituderesulting from the superposition of two waves of slightly different frequencies is known as phenomenon of beats.  
    If m is the number of beats per second, then, m = f1-f2. Here f1 and f2 are the frequencies of the two waves.
    y1 = asin2πf1t, y= asin2πf2t
    y = y1+y2= Asin2πft
    Amplitude, A = 2acos2π(f1-f2/2)t, Frequency, F = f1-f2/2
    (a) Maxima:- t = f/f1-f2
    (b) Minima:- t = 2f+1/2(f1-f2)
  • Beat period (tb):- It is defined as the time interval between consecutive beats or it is the time between two consecutive maxima or minima of intensity of sound.
    tb = 1/f1-f2
    If m is the number of beats per second, then,
    m = 1/beat period = f1-f2
    This signifies, the number of beats per second is equal to the difference in frequencies of two waves.
    Sound Waves:-
    It is the form of energy which produces, in us, the sensation of hearing.
  • Properties:-
    (a) Longitudinal in nature.
    (b) It requires a material medium for its propagation.
    (c) Sound waves can be reflected.
    (d) Sound waves suffer refraction.
    (e) Sound waves show the phenomenon of interference
    (f) Sound waves shows diffraction
    (g) Sound propagates with a velocity much smaller than that of light.
    (h) Sound gets absorbed in the medium through which it passes.
  • Loudness (L)or Intensity (I):-
    L∝logI
    So, L = K log10(I1/I0)
    Unit of intensity of sound is bel.
  • Intensity (I) and Amplitude (A):- I∝A2
  • Intensity(I) and distance from the source (r):- I∝1/r2
  • Pitch or Shrillness:-Pitch is a sensation which determines the shrillness of sound. It is subjective and cannot be measured quantitatively. It depends up on frequency and relative motion between the sources and the listener.
  • Quality or Timber:- It is that characteristic of a musical sound which enables us to distinguish between two notes of the same pitch and loudness produced  by two different sources.
  • Velocity u of longitudinal wave (sound) [Newton’s Formula]:-
    u =√E/ρ
    Here E is the coefficient of elasticity and ρ is the density of medium.
  • Velocity of sound in solids:-
    u =√Y/ρ
    Here Y is the young’s modulus of elasticity and ρ is the density.
  • Velocity of sound in liquids:-
    u =√B/ρ
    Here B is the Bulk modulus of elasticity and ρ is the density.
  • Velocity of sound in gases:-
    u=√γP/ρ
    Here, γ (=cP/cV) is the adiabatic ratio, P is the pressure and ρ is the density.
  • Various factors affecting velocity of sound:-
    (a) Effect of density:- The velocity of sound in a gas varies inversely as the square root of its density. u1/ u2 = √[ρ2/ρ1]
    (b) Effect of moisture:-um/ud= √[ρd/ ρm]
    Since, ρmd, then, um>ud
    This signifies sound travels faster in moist air.
    (c) Effect of pressure:- u=√γP/ρ=√γk = constant
    This signifies, change of pressure has no effect on the velocity of sound.
    (d) Effect of temperature:- ut/u0 =√ρ0t= √T/T0
    Thus, velocity of sound varies directly as the square root temperature on Kelvin’s scale.
    (e) Temperature coefficient of velocity of sound (α):- α = u0/546 = (ut-u0)/t
  • Overtones in open pipe:-An open pipeis openat both ends. Since air is free to vibrate at an open end, we must get an antinode at the open end.
    Waves Class 11 Notes Physics Chapter 14(a) Fundamental frequency:-
    Wavelength,  λ=2l
    Frequency,  f=u/2l = (1/2l)√(γP/ρ)
    Here l is the length of the pipe and u is the velocity of sound.
    (b) First overtone (Second Harmonic):-
    Wavelength,  λ1=l
    Frequency,  f1=2f
    (c) Second overtone (Third Harmonic):-
    Wavelength,  λ2=2l/3
    Wavelength,  f2=3f
  • Overtones in closed pipe:-Since air, at a closed end, is not free to vibrate, there must be a node at a closed end always.
    Waves Class 11 Notes Physics Chapter 14
    (a) Fundamental frequency:-
    Wavelength,  λ=4l
    Frequency,  F=u/4l = (1/4l)√(γP/ρ)
    Here l is the length of the pipe and u is the velocity of sound.
    (b) First overtone (Third Harmonic):-
    Wavelength,  λ1=(4/3)l
    Frequency,  F1=3F
    (c) Second overtone (Fifth Harmonic):-
    λ2=4l/5
    F2=5F
  • Comparison of fundamental frequencies of a closed end of an open pipe:- f = 2F
  • Doppler’s Effect:-Theapparent change in pitch of a note, due to the relative motion between the source and the listener is called Doppler’s effect.
    (a) Source in motion, listener at rest:-
    (i)  Source approaching the listener:-
    Modifying wave length, λ' = V-a/f
    Apparent frequency, f' = [V/V-a]f
    Change in frequency, ?f = (a/V-a)f
    Here V is the velocity of sound in air and a is the velocity of source when it moves towards the listener.
    (ii) Source going away from the listener:-
    Apparent frequency,f' = [V/V+a]f
    Change in frequency, ?f = -(a/V+a)f
    (iii) Source crossing the listener:-
    Apparent frequency of the source before crossing = (V/V-a) f
    Apparent frequency of the source after crossing = (V/V+a) f
    Change in frequency, ?f = -(2aV/V2-a2)f
    (b) Source at rest, listener in motion:-
    (i)  Listener moving away from source:-
    Apparent frequency,f'= [V-b/V]f
    Change in frequency, ?f = (-b/V)f
    Here b is the velocity of listener.
    (ii) Listener moving towards the source:-
    Apparent frequency:-f'= [V+b/V]f
    Change in frequency, ?f = (+b/V)f
    (iii) Listener crossing the source:-
    Apparent frequency of the source before crossing = (V+b/V) f
    Apparent frequency of the source after crossing = (V-b/V) f
    Change in frequency, ?f =-2fb/V
    (c) Source and listener both in the medium:- Change in frequency due to relative motion of source and listener.
     Source (S)#
    Listener (L) (X)
    Nature of velocities
    Expression for f '
    Waves Class 11 Notes Physics Chapter 14
     Waves Class 11 Notes Physics Chapter 14
     +ve, +ve
    f ' = (V-b/V-a) f
    Waves Class 11 Notes Physics Chapter 14
     Waves Class 11 Notes Physics Chapter 14
     +ve, -ve
    f ' = (V+b/V-a) f
     Waves Class 11 Notes Physics Chapter 14#
     Waves Class 11 Notes Physics Chapter 14
     -ve, -ve
    f ' = (V+b/V+a) f
    Waves Class 11 Notes Physics Chapter 14 #
     Waves Class 11 Notes Physics Chapter 14
     -ve, +ve
    f ' = (V-b/V+a) f 

(d) Effect of motion of medium:-
Apparent frequency:-f ' = [(R-b)/(R-a)] f
Here, R = V+ωcosθ, ω is the velocity of wind, θ is the angle between direction of propagation of sound and that of wind.

The document Waves Class 11 Notes Physics Chapter 14 is a part of the NEET Course NCERT Exemplar & Revision Notes for NEET.
All you need of NEET at this link: NEET
182 docs

Up next

FAQs on Waves Class 11 Notes Physics Chapter 14

1. What are waves?
Ans. Waves are disturbances that transfer energy from one place to another without transferring matter. They can be classified into two types: mechanical waves, which require a medium to travel through, and electromagnetic waves, which can travel through a vacuum.
2. How do sound waves work?
Ans. Sound waves are a type of mechanical wave that travels through a medium, typically air. They are created when an object vibrates, causing the surrounding air molecules to vibrate as well. These vibrations then travel as a wave of compressions and rarefactions, which our ears detect as sound.
3. What is the difference between frequency and wavelength of a wave?
Ans. Frequency refers to the number of complete cycles of a wave that pass a certain point in a given time. It is measured in hertz (Hz). On the other hand, wavelength is the distance between two corresponding points on a wave, such as the crest to crest or trough to trough. It is usually measured in meters (m).
4. How does the speed of a wave relate to its frequency and wavelength?
Ans. The speed of a wave is determined by the product of its frequency and wavelength. This relationship is given by the equation v = fλ, where v represents the wave's speed, f is its frequency, and λ is its wavelength. As frequency increases, the wavelength decreases, and vice versa.
5. Can sound waves travel through solids, liquids, and gases?
Ans. Yes, sound waves can travel through solids, liquids, and gases. However, the speed of sound varies depending on the medium it travels through. Generally, sound travels faster in solids than in liquids, and faster in liquids than in gases. This is due to differences in the density and elasticity of the materials.
182 docs
Download as PDF

Up next

Explore Courses for NEET exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Previous Year Questions with Solutions

,

study material

,

Important questions

,

mock tests for examination

,

Semester Notes

,

shortcuts and tricks

,

Waves Class 11 Notes Physics Chapter 14

,

video lectures

,

Waves Class 11 Notes Physics Chapter 14

,

past year papers

,

Summary

,

pdf

,

Extra Questions

,

MCQs

,

Exam

,

Viva Questions

,

Sample Paper

,

practice quizzes

,

Waves Class 11 Notes Physics Chapter 14

,

Objective type Questions

,

Free

,

ppt

;