Chapter 1 Simple harmonic motion & waves Flashcards
Simple harmonic motion & waves
What is simple harmonic motion?
simple harmonic motion is a to-and-fro oscillatory motion in which the acceleration of the body is directly proportional to the displacement of the body from the main position and it is always directed toward the mean position.
Think of several examples in everyday life of motion that are simple harmonic motions.
Example of SHM
(i) motion of a simple pendulum
(ii) motion of a ball in a bowl
(iii) the motion of the mass-spring system
(iv) motion of a pendulum of a clock
What is meant by damped oscillations? How damping progressive reduces the amplitude of oscillation.
The oscillations of a system in the presence of some resistive force are called damped oscillations. for example, Shock absorbers in automobiles are one practical application of damped motion.
vibratory motion of Ideal systems in the absence of any friction or resistance continues indefinitely under the action of a restoring force. Practically, in all systems, the force of friction Retard the motion, so the systems do not osculate indefinitely. the friction reduces the mechanical energy of the system as time passes, and the motion is said to be damped. this damping Progressively reduces the amplitude of the motion.
How can you define the term wave motion?
Wave motion
“wave is a disturbance in the medium which causes the particles of the medium to undergo vibratory motion about their mean position in equal intervals of time.” (OR) “Waves are produced when a body vibrates or oscillates about its mean position”
Difference between mechanical waves and electromagnetic waves
Mechanical waves:
“The waves which require any material medium for their propagation are called mechanical waves.”
Examples:
Water waves, sound waves and waves on spring and spring are called mechanical waves.
Electromagnetic waves:
“the waves with do not require any material medium for their propagation are called electromagnetic waves”
Example:
radio waves, television waves, X-rays, heat waves, light waves etc are electromagnetic waves.
Difference between longitudinal and transverse waves.
Longitudinal waves:
- the weight in which the particles of the medium move back and forth along the direction of propagation of the waves are called longitudinal waves.
- Examples:
Wave moving along a spring sound waves etc.
Transverse waves:
- the wave in which the motion of particles of the medium is perpendicular to the motion of a wave is called transverse wave.
- Examples:
Transverse waves on a slinky, waves on the surface of water, light waves etc.
Define vibratory motion.
The two and slow motion of a body about its mean position is known as vibratory motion.
Example:
the motion of a simple pendulum about its mean position motion, the motion of a see-saw about its mean position, etc.
How a spider detects his prey?
Spider detect his Prey due to vibration produced in its web.
State Hooke’s law and write its equation.
If the force ‘F’ applied on a mass attached to the spring will displace the spring through distance ‘X’, then this force is directly proportional to the change in the length or distance moved by mass ‘m’.
Mathematically, F ∝ x or F = -Kx
Here, the negative sign shows that force is always directed to the mean position.
K is called the spring constant its value is K = -F/x
define elastic restoring force.
The force which pushes or pulls the object performing oscillatory motion towards the mean position is called Restoring force.
Mathematically, restoring force is defined as the following:
F = -kx
Where negative signs show that the force is always directed towards the mean position.
Define a spring constant and write its formula.
“Spring Constant is defined as the ratio of applied force to the change in length of a spring”
Mathematically, the Spring Constant is written as k = F/x
SI unit of spring constant SI unit of spring constant ‘k’ is Nm-1
Write K.E. and P.E. at different positions of a mass-spring system.
At mean position: K.E. = Max, P.E. = 0
at extreme position +A: K.E. = 0, P.E. = Max, At extreme position -A:
K.E. = 0, P.E. = Max
How many times a human eardrum can oscillate in one second?
A human eardrum can oscillate back and forth up to 20,000 times in one second
what is the displacement of an object in SHM when the kinetic and potential energies are equal?
When the object is at rest, its K.E. and P.E., both are zero. Thus, its displacement is zero.
Define a simple pendulum and write its formula for its time period.
A simple pendulum consists of a small bob of mass ‘m’ suspended from a light string of length ‘l’ fixed at its upper end.
The formula of Time Period:
The time period ‘T’ of a simple pendulum of length ‘l’ Is given by the following formula.
T = 2π √l/g
where ‘g’ is the gravitational acceleration of the bob of a simple pendulum.
what is meant by the time period of a simple pendulum?
the time period of a pendulum is the time to complete one cycle or vibration.
what factors do not effect time period of a simple pendulum?
the time period of a pendulum is independent of the mass and amplitude of a simple pendulum.
Define restoring force. In the vibratory motion of a simple pendulum which component of the weight acts as restoring force?
Elastic restoring force:
“The force which pushes or pulls the object performing vibratory motion or oscillatory motion towards mean position is called restoring force.”
Component of a weight that acts as Restoring Force:
“the restoring force that causes the pendulum to undergo simple harmonic motion is the component of gravitational force ‘mg sinθ’ tangent to the path of motion”
Tell whether or not these motions are examples of simple harmonic motions.
(a) the up and down motion of a leaf in a water pond.
(b) motion of the ceiling fan.
(c) motion of hands of the clock.
(d) motion of a plucked string fixed at both ends
(e) movement of honey bees.
a) the up and down motion of a leaf in a water pond. (Yes)
(b) motion of the ceiling fan. (No)
(c) motion of hands of the clock. (Yes)
(d) motion of a plucked string fixed at both ends. (Yes)
(e) movement of honey bees. (No)
Characteristics/features of a simple harmonic motion.
(i) A body executing SHM vibrates about a fixed position; called the mean position.
(ii) Its acceleration is always directed towards the mean position.
(iii) The magnitude of the acceleration is always directly proportional to its displacement from the mean position i.e., acceleration will be zero at the mean position while it will be maximum at extreme positions.
(iv) Its velocity is maximum at the mean position and zero at extreme positions.
What is meant by vibration?
One complete round trip of a vibrating body about its mean position is called one vibration.
What is meant by frequency? Write its SI unit.
“The number of vibrations or cycles of a vibrating body completed in one second is called frequency ‘f’ “
The si unit of frequency is vibration per second or cycles per second or HZ.
Define time period.
“Time taken by a vibratory body to complete one vibration is called time period” It is denoted by T
Define amplitude.
“The distance of the particles of the stretched string from its rest position or mean position is called amplitude”
What is the relation between frequency and Time Period?
Mathematically; frequency ‘f’ is reciprocal of time period ‘T’
i.e. f = 1/T
What is meant by wavelength?
For Longitudinal Waves:
“The distance between two consecutive compressions or rare fractions is called wavelength.”
For Transverse Waves:
“The distance between two consecutive crests or troughs is called wavelength.”
Define wave motion.
“A Wave is a disturbance in the medium which causes the particles of the medium to undergo vibratory motion about their mean position in equal intervals of time”
How are crests and troughs produced in water waves?
Dip one end of a pencil into a tub of water, and move up and down vertically, the disturbance in the form of ripples produces water waves, which move away from the source.
When the waves reach a small piece of cork floating near the disturbance, it moves up and down about its original position while the wave will travel outwards. The net displacement of the cork is zero. The cork repeated its vibratory motion about its mean position.
What are the main types of waves?
(i) Mechanical waves
(ii) Electromagnetic waves
Define Mechanical Waves.
“The waves which require any material medium for their propagation are called mechanical waves. “
Example:
Water waves, sound waves, waves on a spring and string are called mechanical waves.
Define electromagnetic waves.
“The waves which do not require any material medium for their propagation are called electromagnetic waves”
Example:
Radio waves, television waves, X-rays, heat waves, light waves, etc.
Types of mechanical waves.
(i) Longitudinal mechanical waves
(ii)Transverse mechanical waves
Define Longitudinal waves.
“The waves in which the particles of the medium move back and forth along the direction of propagation of the wave are called longitudinal waves.”
Example: Waves moving along a spring, sound waves, etc.
In which medium speed of longitudinal waves?
Longitudinal waves move faster through solids than through liquids and gases.
Why the speed of transverse waves in solids is less than half the speed of longitudinal waves?
Transverse waves move through solids at a speed of less than half of the speed of longitudinal waves. It is because the restoring force exerted during this up-and-down motion of particles of the medium is less than the restoring for exerted by a back-and-forth motion of particles of the medium in the case of longitudinal waves.
Define transverse waves.
The waves in which the motion of particles of the medium is perpendicular to the motion of a wave are called transverse waves.
Differentiate between the crest and trough of transverse waves.
Crests:
The crests are the highest points of particles of the medium form the mean position.
Troughs:
The troughs are the lowest points of the particles of the medium from the mean position.
Define mechanical waves and why these waves cannot pass through the vacuum.
Mechanical waves require a medium for their propagation. So, they cannot pass through the vacuum.
What are the factors on which the amount of energy carried by the waves depends?
The amount of energy carried by the wave depends upon the following factors:
(I) Amplitude:
The greater the amplitude of a wave, the greater the amount of the energy transferred by the wave.
(ii) Frequency:
If we shake the string faster, we give more energy per second to produce a wave of higher frequency, and the wave delivers more energy per second to particles of string as it moves forward.
Why does a high-frequency wave carry more energy than a low-frequency wave?
To generate a high-frequency wave requires more energy per second than to generate
a low-frequency wave. Thus, a high-frequency wave carries more energy than a low-frequency wave of the same amplitude.
How do geophysicists learn about the internal structure of Earth? (OR) what are seismic waves and their advantage?
An earthquake produces waves through the body of the earth in the form of seismic waves. by studying such waves, Geophysicists learn about the internal structure of the earth and information about the occurrence of future Earth activity.
What do the dark and bright fringes on the screen of the ripple tank represent?
Water waves are transverse waves. the bright fring on the screen of represent represents a crest while the dark fring represents a trough.
What is a ripple tank?
(OR) what do you know about ripple tanks?
(OR) what is the function of a ripple tank?
It is a device used to produce and study the characteristics of water waves.
What is meant by the reflection of waves?
When waves moving in one medium fall on the surface of another medium, they bounce back into the first medium such that the angle of incidence is equal to the angle of reflection this phenomenon is called reflection of waves.
Define the diffraction of waves.
“The bending or spreading of waves around sharp edges or corners obstacles is called a diffraction”
Define the wave equation and write down its formula.
The relationship between velocity (v), frequency (f) and wavelength (λ) of the wave is called a wave equation.
Formula: Mathematically, the wave equation is given as
v = fλ
