Mechanics 4 Flashcards
What are the conditions for the medium for a mechanical wave to propagate through it?
Should be elastic
Resistance of medium should be small
Define a mechanical wave
A mechanical wave can be considered as and oscillatory disturbance traveling through a medium without change in form.
Define transverse waves
The waves in which the particles of medium vibrate in a direction perpendicular to the direction of propagation of waves are called transverse waves.
Define longitudinal waves
The waves in which the particles of the medium vibrate in a direction parallel to the direction of propagation of waves are called longitudinal waves,
Define amplitude of a wave
The maximum displacement of any particle from thE mean position is called the amplitude of the wave.
Define Period of a wave
The time taken by any particle to complete one vibration is known as the period of the wave.
Define frequency of a wave
The number of vibrations per second by a particle is called the frequency of the wave.
Define wavelength of a wave
The distance between two consecutive particles of the medium which are in the same phase or differ in phase by 2pi radians is called wavelength of the wave.
Define velocity of the wave
The distance travelled by the wave in one second is called the velocity of the wave.
Explain double periodicity of a wave
Form of wave repeats itself in equal intervals of time- periodic in time
Form of wave repeats itself at equal distances- periodic in space
Defined progressive waves
Progressive waves are waves which continuously travel in a given direction
How much phase difference does a path difference of x correspond to?
2π*x/λ
Give the expression for representing a one dimensional simple harmonic progressive wave traveling in the direction of the positive x-axis.
y= asin[ω(t-(x/v))]
Or
y= asin[2π((t/T)-(x/λ))]
Give the expression for representing a one dimensional simple harmonic progressive wave traveling in the direction of the negative x-axis
y= asin[ω(t+(x/v))]
Or
y= asin[2π((t/T)+(x/λ))]
Why is a small surface sufficient for reflection of light waves whereas a large surface required for reflection so found waves?
Wavelength of light waves- angstrom
Wavelength of light waves- mm
What happens when a transverse wave is reflected from a fixed surface?
Crest becomes trough
Trough becomes crest
What happens when a transverse wave is reflected from a free surface? (Rarer medium)
Crest remains crest
Trough remains trough
What happens when a longitudinal wave is reflected from a fixed end? (Denser medium)
Compression remains compression
Rarefaction remains rarefaction
What happens when a longitudinal wave is reflected from a eared medium?
Compression reflected back as rarefaction
Rarefaction becomes compression
What is change of phase of a wave incident on the boundary of a denser medium?
Phase changes by π radian
State the principle of superposition of waves
The principle of superposition of waves states that when two or more waves traveling through a medium arrive at a point of the medium simultaneously, each wave produces its own displacement at the t point independently of the others. Hence the resultant displacement at that point is equal to the vector sum of the displacement due to all the waves.
Define constructive interference
If two transverse waves superimpose in phase then a crest due to one coincides with a crest due to other or a trough due to one coincides with a though due to the other, then the resultant amplitude at that point is maximum and is called constructive interference.
Define destructive interference
If a crest due to one waves coincides with a trough due to the other, or vice versa, the resultant amplitude due to interference is minimum and is called destructive interference.
explain Quincke’s Tube experiment
nλ= constructive (n+(1/2))λ= destructive
When is the sound of beats said to wax and wane?
When the sound becomes loud (max) it is said to wax and when the sound becomes faint (min) it is said to wane.
Define production of beats
The waxing and waning of sound after definite intervals of time, due to superimposition of two waves of nearly equal frequencies is called production of beats.
Define frequency of beats
The number of times sound waxes or wanes in one second is called frequency of beats.
Application of beats
Used to determine unknown frequency.
Tuning of musical instruments.
To produce low frequency notes in jazz orchestra or western music.
Detect presence of dangerous gases in mines.
Superheterodyne oscillators - makes tuning of receivers simple.
How do beats help in detection of dangerous gases that may be present in mines?
Speed of sound diff in diff media.
Pg 114
What is Doppler effect?
Whenever there is relative motion between the source of sound and and observer, there is and apparent change in frequency of sound emitted by the source and as heard by the observer. This is called Doppler effect.
General formula for Doppler effect
n’= ((v+/- vo)/(v-/+ vs))*n
Applications of Doppler effect
Color Doppler sonography Speed detection on highways RADAR speed of star ( moving towards - towards violet, moving away - towards red) Speed of rotation of sun
Limitations of Doppler effect
Applicable only when velocities of source of sound and observers are much less than velocity of sound.
Motion must be along same straight line
Medium must be at rest else modifications on formula required
What happens when a wave traveling through denser medium arrives in the surface of rarer medium?
If wave traveling through denser medium arrives in the surface of rarer medium direction of wave velocity is reversed but direction of particle velocity is not reversed.
Phase diff zero
Define stationary waves
When two identical progressive waves bother transverse or longitudinal traveling along the same path in opposite directions, interfere with each other and by superposition of waves resultant wave is obtained in the form of loops and is called a stationary wave.
How do the frequency and amplitude if a stationary wave vary?
Frequency same as that of progressive wave but amplitude varies with position of particle.
Define antinodes
The points of the medium which vibrate with maximum amplitude are called antinodes.
Define nodes
The points of the medium which vibrate with minimum amplitude are called nodes.
Distance between any two nodes or antinodes
λ/2
Distance between any node and adjacent antinode
λ/4
Properties of stationary waves
Definition
Nodes and antinodes
Dist between two successive nodes or antinodes
Dist between adjacent node and antinode
Particles within the loop are in the same phase of vibration
Particles in adjacent loops are vibrating out of phase
Stationary wave is a doubly periodic phenomenon
Resultant wave velocity is zero, no transfer of energy through medium
Pressure nodes and antinodes
What are pressure antinodes?
Points at which displacement of particle is minimum but variation in pressure is maximum are called pressure antinodes.
What are pressure nodes?
Points in a longitudinal stationary wave at which displacement of particle is maximum but pressure is constant are called pressure nodes.
What is a harmonic?
The word harmonic is used to indicate the fundamental frequency and all it’s integral multiples.
What does the word overtone refer to?
The word overtone is used to indicate only those multiples of fundamental frequency which are actually present in the given sound.
Equation for Velocity of a transverse wave on a string
V= root(T/m)
What is a mode ?
The vibrations corresponding to each note is called a mode.
What is the fundamental mode?
The mode of vibration corresponding to the first harmonic is called fundamental mode.
General formula of frequency of pth overtone of a vibrating string
n’= (p+1) n = (p+1)(1/2l)root(T/m)
Laws of vibrating strings
Law of length
Law of tension
Law of linear density
State the law of length of a vibrating string
The fundamental frequency of transverse vibrations if a stretched string is inversely proportional to the vibrating length if the string if the tension in the string ‘T’ and linear density ‘m’ of the string are kept constant.
State the law of tension of a vibrating string
The fundamental frequency of transverse vibrations of a stretched string is directly proportional to the square root of the tension in the string if the linear density ‘m’ and the vibrating length ‘l’ are kept constant.
State the law of linear density (law of mass per unit length)
The fundamental frequency of transverse vibrations of a stretched string is inversely proportional to the linear density of the string if the vibrating length ‘l’ and tension in the string ‘T’ are kept constant.
Define specific gravity or relative density
It is the ratio of density of substance to density of water.
What is a closed organ pipe?
A cylindrical tube having and air column with one end closed.
Necessary condition for modes of vibration in an open organ pipe
Time taken to produce a compression and a rarefaction is equal to time taken by the wave to travel twice the length of the tube.
Boundary condition for closed organ pipe
Closed end is always displacement node (Or pressure antinode) and open end is always displacement antinode (or pressure node).
Fundamental frequency of vibration for closed end organ pipe
n= v/4L
What are the harmonics present in closed organ pipe?
1,3,5…. Only odd harmonics
Boundary condition for open organ pipe
Antinodes are always at both open ends of pipe (it is pressure node point).
Fundamental frequency of open organ pipe
n= v/2L
What harmonics are present in and open end organ pipe?
1,2,3… All harmonics are present as overtones
Compare quality of sound from open organ pipe and closed organ pipe.
Richer in open due to more overtones.
Define end correction
Distance between open end of an air column and antinode is called end correction.
Formula for end correction
e=0.3d
What is the cause for end correction?
Air particles in the plane of the open end of the tube are not free to move in all directions. Hence, reflection takes place at the plane a small distance outside the tube.
Limitations of end correction
Inner diameter of tube must be uniform throughout its length.
Effect of flow of air outside tube is to be neglected.
Effect of temperature of air outside to be neglected.
Timp of the prong of vibrating tuning fork must be held horizontally (perpendicular to resonance tube) at centre and at a small distance above open end of the tube.
What are free vibrations and what is natural frequency?
When a body capable of oscillating is displaced from its stable equilibrium position and released, it makes oscillations which are called free vibrations (free oscillations) and the frequency of vibrations is called its natural frequency.
Define forced vibrations
The vibrations of body under the action of an external periodic force in which the body vibrates with a frequency equal to the frequency of external periodic force (driving frequency) other than its natural frequency are called forced vibrations.
Define resonance
The phenomenon in which the body vibrates under the action of an external period force whose frequency is equal to the natural frequency of the driven body, so that the amplitude becomes maximum is called resonance.
What happens when two identical pendulums are suspended side by side from a flexible horizontal support
Phase diff π/2 rad
Response of B to forced vibrations depends on relative length of two pendulums
Best response (resonance) is observed at equal lengths
Pg 128-129
Explain stethoscope and acoustic stethoscope
Pg 129
Examples of resonance
Two pendulums Stethoscope Tuning of a radio receiver Sonometer Melde's experiment
In Melde’s experiment, give the expression for frequency of the tuning force
I. If vibrations of prongs are parallel to the direction of propagation of the wave
N= 2n= (1/ L)root(T/m)
II. If vibrations of tuning fork are perpendicular to the direction of propagation of the wave
N= n= (1/ 2L)root(T/m)
Applications of resonance
Determining unknown frequency
Tuning of radio
Resonance tube- calculating velocity of sound in air
Hollow wooden box in musical instruments
Increase the intensity of sound in musical instruments
Analyze musical note
Give the disadvantages of resonance
Soldiers ordered to break their step on suspension bridges
Clapping of hands of audience same f as roof— then dadadaaaaahhh
When speed of aircraft increases, parts vibrate resonance is undesirable
In sea if natural frequency of swinging ship= frequency of water waves…
Musical instruments can be classified as:
Stringed instruments
Wind instruments
Percussion instruments
Solid instruments
Examples of string instruments in which string is struck by hammer
Pianoforte, santoor
Examples of string instruments in which string is plucked by hand
Sitar, veena, guitar, tanpura.
Why do the violin and sitar note having same frequency appear to be different?
Different number of overtones accompanying them.
Examples of wind instruments
Flute
Bugle
Basoon
Harmonium
Explain flute
Cylindrical pipe of either metal or bamboo closed at one end.
One narrow opening + 7holes
Pg 130
Explain bugle
No reeds
Pipe instrument
Bassoon
Pipe instrument with reeds
Explain harmonium
Reed instrument
Without a pipe
Keyboard- air set into vibrations by means of thin metal reeds
Three and a half octaves, 41 reeds
What are reeds in harmoniums?
Fastened at one end of the block in which there is a hole behind the reed can vibrate freely.
What are bellows of a harmonium?
When the wind is forced through the aperture underneath a reed and a key is pressed down, the blast of air (bellows) sets the reeds into vibrations and produces a fairly loud sound.
Give examples of percussion instruments
Drums, tabla, mridangam
