Chapter 10: General Waves Properties
10.1 Waves and Nature of Waves
Q: Wave motion transfers energy without moving matter. Justify this statement with an example.
For example: When a wave moves through a rope, the energy is transferred along the rope, causing the particles to vibrate, but the overall position of the rope does not change. The wave moves the energy, not the matter.
Q: What is the main difference between mechanical waves and electromagnetic waves?
The main difference between Mechanical waves and electromagnetic waves are:
Medium of Propagation
- Mechanical waves require a medium for propagation, such as a solid, liquid, or gas.
- Electromagnetic waves do not require a medium and can travel through a vacuum, such as space.
Nature of Wave
- Mechanical waves are disturbances in a physical medium,
- Electromagnetic waves are oscillations in electric and magnetic fields.
Speed
- The speed of mechanical waves is determined by the properties of the medium,
- The speed of electromagnetic waves is always the same (the speed of light).
Interaction with Matter
- Mechanical waves can be absorbed, reflected, or refracted by matter,
- Electromagnetic waves can pass through most matter with little interaction.
10.2 Properties of Waves
Q: How are spherical wavefronts produced in the ripple tank?
When a spherical dipper is attached to the vibrator, circular waves are produced. These waves have circular wavefronts.
Q: What is the difference between the displacement and amplitude of the wave?
The difference between Displacement and amplitude is:
Displacement
The displacement of a wave is the maximum distance a particle of the medium moves from its rest position. It is a measure of how far a particle has been moved from its equilibrium position.
Amplitude
The amplitude of a wave is the maximum height or depth of the wave from its rest position. It is a measure of the strength or energy of the wave.
In short, displacement describes the position of a particle in a wave, while amplitude describes the height or strength of the wave.
Q: Drive the relation between wave speed and frequency.
Relation between wave speed and frequency
Since
`Speed` `=` `\frac(distance)(time)`
`v` `=` `\frac(S)(t)`
For a wave:
Distance travelled `(S)` `=` Wavelength `(\lambda)`
Time taken `(t)` `=` Time Period `(T)`
`v` `=` `\frac(\lambda)(T)`
We know that:
`f` `=` `\frac(1)(T)`
put in above equation:
`v=f\lambda`
10.3 Simple Harmonic Motion (SHM)
Q: Calculate the frequency of the second pendulum?
The frequency of a simple pendulum is given by the equation:
`f=1\div2\pi\sqrt{\frac (l)(g)}`
where `f` is the frequency, `l` is the length of the pendulum, `g` is the acceleration due to gravity (`9.8` `\frac (m)(s^2)` at the surface of the Earth),
and `\pi` is pi (approximately 3.14).
For a pendulum with a length of 1 meter, the frequency would be:
`f=1\div2\pi\sqrt{\frac (1)(9.8)}`
`f=1\div2\pi\sqrt{0.102}`
`f=1\div2\pi\times\left(0.319\right)`
`f = 1 / 0.5 = 0.5 Hz`
So, the frequency of a 1-meter-long pendulum is approximately `0.5` cycles per second.
Q: Which force component (weight) is responsible for the oscillatory motion of a simple pendulum?
The perpendicular component of weight is responsible for the oscillatory motion of a simple pendulum.
This component is also known as the restoring force and acts in the opposite direction to the displacement of the pendulum.
The restoring force can be mathematically expressed as `-mgSinθ`
where `m` is the mass of the pendulum, `g` is the acceleration due to gravity, and `θ` is the angle of displacement from the vertical.
The negative sign indicates that the restoring force acts in the opposite direction to the displacement.
Q: At what position acceleration of the simple oscillatory pendulum is maximum, and why?
A simple pendulum executes simple harmonic motion. It is directly proportional to the displacement. Therefore, the acceleration of a simple oscillatory pendulum is maximum at its extreme positions.
Q: The typical reaction of the bowl on the ball is in the upward direction. Why is it not moving in that direction?
At the mean position, the normal reaction force of the bowl on the ball is balanced by the weight of the ball. At a displaced position, this normal reaction force is balanced by a component of weight `(mgSinθ)`. That is why the ball does not move in the direction of normal reaction force.
Q: Where is the ball in the bowl system moving fastest, slowest?
In a ball-in-bowl system, the ball moves fastest at its lowest point and slowest at its highest point.
This is because the velocity of an oscillating object is proportional to the displacement from its equilibrium position.
At the lowest point, the displacement is minimum and the velocity is maximum, resulting in the ball moving fastest.
At the highest point, the displacement is maximum and the velocity is zero, resulting in the ball moving slowest.
10.5 Damped Oscillation
Q: What will happen if there is no damping in an oscillating drum skin?
If there is no damping in an oscillating drum skin, the amplitude of oscillation will remain constant and it will continue to vibrate at its resonant frequency indefinitely.
No energy will be lost, so the sound produced by the drum skin will persist without fading away.
Chapter 10: General Waves Properties
MCQs | Notes | Numerical | Self Assessment Questions
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