Waves High Yield Notes PDF

WAVES High Yield Notes  NOTES NOTES WAVES "Disturbance created in a medium" It is the transfer of energy and momentum without tran...

WAVES High Yield Notes  NOTES NOTES WAVES "Disturbance created in a medium" It is the transfer of energy and momentum without transfer of mass and matter. Types of Waves : Electromagnetic Mechanical Waves Matter Waves Waves waves associated doesn't requires requires medium with electrons medium propagate through propagate due to oscillations of medium oscillation of E.f and particles M.f E.g; sound waves, E.g; heat, light, radio string waves, E.g; X-rays wave etc water waves Electric field Y osscilation Vibration P Travel Propagation Necessary conditions of wave motion: Medium must be elastic. Particles of medium should not be independent of each other. 1 PreMed.PK  NOTES Types Of Mechanical Waves Shock Waves Stationary Waves Travelling Waves waves produced due to Waves produce in regular/rhythmic the form of pulse waves in which disturbance for very short energy stands in medium and travels period of time between two points away from source of Vobj > Vsound medium Node Wavelength Antinode Amplitude Important: Crest of wave acts as convex lens. Trough of wave acts as concave lens. 2 PreMed.PK  NOTES Progressive Waves Transverse Waves Longitudnal Waves direction of propagation of wave is direction of propagation of waves held perpendicular to vibration of is along the vibration of particle particles θ=90° θ=180° or 0° compression and rarefaction made: crest and trough are made: Compression; crowding of Crest; portion above mean level particles is max. Trough; portion below mean level Rarefaction; crowding of paeticles is min. E.g; water waves, Light waves E.g; sound waves Crest Compresion Rarefaction Trough Both waves can be set up in solids. In fluids,transverse waves dies out quickly. Transverse waves cannot propagate through gases. 3 PreMed.PK  NOTES Properties of waves Wavelength: “Distance between 2 consecutive crest and trough.” distance between 2 consecutive compression/ rarefaction — λ distance between 2 alternate compression/ rarefaction—2λ distance between compression and rarefaction—λ/2 Time Period: “Time required to complete 1 vibration” 1 crest + 1 trough = 1 vibration Relation Between Phase Difference and Path Difference θ = 2π / λ × path diff where, Path diff = λ / 2 In phase points: P.d = nλ where it can be 0,λ,2λ,3λ …….. (integers)… θ= 2πn where it can be 0,2π,4π……. (even) n is 0,1,2,3… Out of phase points: P.d = (n+1 /2) λ where it can be λ/2, 3λ/2, 5λ/2..… (fractions) θ= 2π(n+1|2) where it can be π,3π,5π……(odd) 4 PreMed.PK  NOTES Speed of waves Speed Of Waves: V=f λ where; v = velocity , f = frequency λ = wavelength When medium remains same; Frequency → changes Velocity → constant f ∝ 1/λ When medium changes; Frequency → constant Velocity → changes V ∝ λ v= f λ. = n/t. λ = λ/t n=c/v where, n=refractive index c=speed of light v=velocity For air, n=1 so v=3 ×10⁸ For water, n=1.33 so v=2.5× 10⁸ For glass, n=1.5 so v=2× 10⁸ Wave Medium Velocity λ Phase rare to increase increase 180 Mechanical Waves denser E.g. sound waves denser to decrease decrease 0 rare Electromagnetic rare to decrease decrease 180 waves denser E.g; light denser to waves increase increase 0 rare 5 PreMed.PK  NOTES Speed of Sound in AIr Sound waves → longitudinal waves V=280m s⁻¹(theoretical) v=332m s⁻¹ at 0°C V=332m s⁻¹ (original) diff=52 Types Of Sound Waves: error=16% audible (20Hz– 20,000Hz) Laplace Formula: infrasonic (f ˂ 20Hz) based on adiabatic process ultrasonic (f ˃20kHz) (heat=const) supersonic ( greater than speed E adiabatic = γP of sound) V=√γP ∕ ρ v=333m s⁻¹ (theoretical) v=332m s⁻¹ (original) Animals f of sound diff=1 error= less than 10% Dolphin 150-150,000 Hz Bat 1000-120,000 Hz Factors Affecting Speed Of Sound: Dog 15-50,000 Hz Pressure, no effect of pressure on the speed of soun (by Cat 60-70,000 Hz increasing or decreasing the pressure, the speed of sound will not change) Human 20-20,000 Hz Density, V=√γP ∕ ρ Important: ∝ so, V 1/√ρ Sound waves produce reflection, V hydrogen > V oxygen refraction, interference, diffraction V hydrogen=4 V oxygen but not polarization. V moist air > V dry air ρ moist < ρ dry Dependence: Temperature, Interia=density V=√γRT∕ M Compressibility=elastic modulus v=√E ∕ ρ ∝ so, V √T T’ = n²T V solids > V gases where; (ρsolids > ρgases) n= no of times speed changes (E solids >> E gases) T= given temperature (absolute T) Newton‘s Formula For T’= new temperature Speed Of Sound: Vt=Vo + 0.61t based on isothermal process Vo= velocity at 0°C =332m|s (temp=const) Relation Between Intensity and E iso = Pressure Amplitude: V=√P ∕ ρ Intensity∝ (Amplitude)2 Amplitude ∝ √intensity 6 PreMed.PK  NOTES Superposition of Waves “When 2 or more waves travels in same direction then amplitude of resultant wave is equal to algebraic sum of 2 waves” waves traveling in same direction= amplitude increase.waves traveling in opposite direction= amplitude decrease Constructive Interference: Wave 1 Wave 2 Destructive Interference: Wave 1 Wave 2 Results Of Superposition Of Waves: Beats Interference Stationary Waves different frequency similar frequency similar frequency same direction of waves , opposite waves, same direction wave direction 7 PreMed.PK  NOTES Beats “When two objects vibrate with different frequencies, you hear a fluctuating sound (soft and loud sound alternatively). This phenomenon is known as beats or beats frequency of sound.” The number of beats produced per second is called beat frequency, which is equal to the difference in frequencies of two waves. fb = |f1 – f2| fb = beats frequency f1 = frequency of sound wave 1 f2 = frequency of sound wave 2 When the diff becomes greater than 10 Hz, it becomes difficult to recognize beats. 8 PreMed.PK  NOTES Interference of Waves Interference: “ 2 same waves traveling in same direction” It is of 2 types; Constructive Interference: “The interference is said to be constructive interference if two waves having the same frequency meet in such a way that the crest of a wave meets the crest of another wave.” The amplitude of sound waves are added so the resultant sound is much louder than that of the original sound. P.d=nλ n=0,±1,±2…….. Destructive Interference: “The interference is said to be a destructive interference if two waves having the same frequency meets in such a way that the crest of a wave meets the trough of another wave.” the amplitude of the sound waves are subtracted so the resultant sound is much weaker than that of the original sound. P.d=(n+1|2)λ Important Echoing zone: region of constructive interference Silence zone : region of destructive interference 9 PreMed.PK  NOTES Stationary Waves “Superposition of 2 waves having Stationary Waves On the same frequency traveling in Stretched String: opposite directions.” They are so called because v=√ F/m there is no flow of energy along where; wave. F= tension in the string Stationary waves consists of m= linear mass density ⇢ m=M|L node and antinode. (kg|m) Node= fixed points. Fundamental frequency: (basic Antinode= open ends tone) f1=√ v/2l f1=1/2l √ F/m Antino Property Node Speed of sinusoidal wave de depends upon tension in the string. Displaceme 0 max. ∝ f √ F/A nt Whenever temperature increases, velocity increases so fundamental frequency also Energy 0 max. increases. If no of loop increases, Stress max. min. wavelength decreases 𝜆∝ 1/n Strain max. min. General Formula: fn=nf1 Pressure max. min. 𝜆 =2l/n where; n= no of harmonics Tension max. min. f1= fundamental frequency overtone = harmonics - 1 NODE > ANTINODE Node λ Antinode distance b/w 2 consecutive node|antinode= λ / 2.distance b/w consecutive node and antinode= λ / 4 10 PreMed.PK  NOTES 1st Harmonic 2nd Harmonic 3rd Harmonic fundamental frequency 1st overtone 2nd overtone plucked from the center plucked from 1|4 th plucked from 1|6 th no of loops=1 no of loops=2 no of loops=3 no of antinode=1 no of antinode=2 no of antinode=3 no of node= 2 no of node=3 no of node=4 STATIONARY WAVES IN f=2fc AIR COLUMN: at open ends=antinodes are formed Open pipe: at closed ends= nodes are formed f°=v/2l Open Pipe: all harmonics exist (odd +even) f0=v/2l rich in harmonics General formula; Close pipe: ＞ Antinodes Nodes fc=v/4l fn=nf1 , 𝝀= 2l /n only odd harmonics exists poor in harmonics 1st Harmonic 2nd Harmonic 3rd Harmonic basic tone 1st overtone 2nd overtone no of antinode= 2 no of antinode= 3 no of antinode= 4 no of node= 1 no of node= 2 no of node= 3 Fundamental frequency 1st Overtone 2nd Overtone f1 f2 = 2f1 f3 = 3f1 l = 1/2 𝝀 l=𝝀 l = 3/2 𝝀 11 PreMed.PK  NOTES Close Pipe: fc=v/4l Antinodes=Nodes General formula; fn=nf1 , λ= 4l |n 1st Harmonic 3rd Harmonic 5th Harmonic basic tone 1st overtone 2nd overtone no of antinode= 1 no of antinode= 2 no of antinode= 3 no of node= 1 no of node= 2 no of node= 3 Fundamental frequency 3rd Overtone 5th Overtone f1 f3 = 3f1 f5 = 5f1 l = 1/4 𝝀 l = 3/4 𝝀 l = 5/4 𝝀 12 PreMed.PK  NOTES Doppler's Effect “Apparent change in frequency of Case#5 :observer is chasing sound|light due to relative motion source b|w source and observer” f’=( v - vo/ v - vs)f If direction is same 𝝀’ =( v -vs/ v + vo) 𝝀 →v →vo Case#6: source is approaching v relative= v - vo towards observer If direction is opposite →v f’=( v - vo/ v - vs)f ←vo 𝝀’ =( v -vs/ v - vo) 𝝀 v relative= v + vo Case#7: observer and source Doppler's Shift: are moving towards each other “ Apparent change in motion of f’=( v + vo/ v - vs)f wavelength due to motion of 𝝀’ =( v -vs/ v + vo) 𝝀 source” Case#8 observer and source are Δλ=vs/F moving away from each other f’=( v ± v°| v ± vs)f f’=( v - vo/v + vs)f f’=apparent frequency 𝝀’ =( v +vs/ v - vo) 𝝀 f=real frequency v=speed of sound v°=speed of observer Applications Of Doppler's vs= speed of source Effect: Case#1: observer moves towards In RADAR (Radio detection and stationary source ranging): f’=( v + vo/ v - vs)f to detect direction, speed and f’=( v + vo/ v )f height of aeroplane 𝝀’ =( v - vs/v + vo) 𝝀 radiowaves are used(travel λ’=( v /v +vo) λ several cm) Case#2:observer moves away In SONAR (Sound navigation from stationary source and ranging): f’=( v -vo/ v )f to find depth of oceans and λ’=( v / v -vo) λ to detect underwater objects Case#2:observer moves away ultrasonic waves are from stationary source used(travels many km) f’=( v -vo/ v )f In ASTRONOMY: λ’=( v /v -vo) λ object moving towards earth Case#3: stationary observer and shows blue shift source is moving towards object moving away from observer earth shows red shift f’=( v / v - vs)f stationary object shows 𝝀’ =( v - vs/v ) 𝝀 yellow shift) Case#4: source is moving away from stationary observer f’=( v / v +vs)f 𝝀’ =( v +vs/v ) 𝝀 PreMed.PK 13  NOTES In RADAR speed trap: to detect speed of vehicle microwaves are used Dopplers effect can be used to monitor blood flow through major arteries.Ultrasonic waves of 5MHz to 10MHz are directed. Bats use echo- location to navigate and find food in the dark. 14 PreMed.PK