General Waves Properties

When water waves pass from deep to shallow regions, their frequency remains constant. This is because the frequency of a wave is determined by the source and does not change with the medium's depth.

Mass is not a characteristic of a wave. Waves are characterized by properties such as amplitude, period, frequency, wavelength, and velocity.

In simple harmonic motion, the maximum speed occurs when the object is at its equilibrium point because the restoring force and acceleration are zero, and kinetic energy is at its maximum.

The bob accelerates from its extreme position due to the gravitational force, which acts as the restoring force in a simple pendulum.

In the ball and bowl system, the mean position is at the center of the bowl, where the ball would naturally come to rest in the absence of any oscillations.

Oscillations are damped due to the presence of frictional forces, which dissipate energy from the system, gradually reducing the amplitude of the oscillations.

A transverse wave is characterized by particles vibrating at right angles to the direction of wave motion.

Crest and trough are features specific to transverse waves, representing the highest and lowest points of the wave, respectively.

In a longitudinal wave, particles move in the same direction as the wave motion, creating compressions and rarefactions.

The main parts of a longitudinal wave are compressions, where particles are close together, and rarefactions, where particles are spread apart.

A mechanical wave requires a medium to travel through, as it relies on the vibration of particles within that medium.

Electromagnetic waves do not require a material medium to travel; they can travel through a vacuum.

When a water wave travels from deep to shallow water, its wavelength and speed decrease due to the interaction with the bottom surface.

The bending of waves around obstacles is called diffraction. This phenomenon is prominent when the size of the obstacle is comparable to the wavelength of the wave.

A simple pendulum shows Simple Harmonic Motion (SHM) when displaced by a small angle, where the restoring force is proportional to the displacement.

The time period of a simple pendulum depends on its length and the local acceleration due to gravity. It is independent of the mass of the bob and the material.

In a damped oscillating system, the amplitude gradually decreases over time due to the dissipation of energy, often through frictional forces.

A wave is a transfer of energy without the transfer of matter. Waves can travel through a medium by causing particles to vibrate, but the particles themselves do not move permanently from their positions.

A water wave is an example of a transverse wave, where the motion of the wave is perpendicular to the direction of particle displacement.

In a transverse wave, the direction of wave motion is perpendicular to the direction of particle vibration.

The SI unit of amplitude is the meter (m), as amplitude measures the maximum displacement from the equilibrium position.

A trough is the lowest point in a transverse wave, opposite to the crest, which is the highest point.

Moving a slinky up and down causes transverse waves, where the coils move perpendicularly to the direction of wave propagation.

Longitudinal waves move parallel to the direction of particle vibration, creating compressions and rarefactions in the medium.

A sound wave is a common example of a longitudinal wave, where the particles of the medium vibrate parallel to the direction of wave travel.

Compression in a longitudinal wave occurs when the coils or particles of the medium are close together, representing a region of high pressure.

Electromagnetic waves can travel through a vacuum, unlike mechanical waves which require a medium.

Microwaves are not mechanical waves; they are a type of electromagnetic wave.

Electromagnetic waves are produced by changing electric and magnetic fields. These fields oscillate perpendicular to each other and to the direction of wave propagation.

The speed of electromagnetic waves in a vacuum is approximately \(3 \times 10^8\) meters per second, commonly known as the speed of light.

Light, radio, and microwave energy are all types of electromagnetic waves, which consist of oscillating electric and magnetic fields.

A ripple tank is used to visualize wave patterns in water, demonstrating properties such as reflection, refraction, diffraction, and interference.

In a ripple tank, waves are visualized as crests and troughs, appearing as bright and dark lines respectively, due to the reflection of light.

After a wave passes in a ripple tank, the water particles return to their original position, demonstrating that waves transfer energy, not matter.

When a wave moves from deep to shallow water at an angle, it changes direction due to refraction. This occurs because the part of the wave in shallow water slows down, causing the wave to bend.

The law of reflection for water waves states that the incident angle is equal to the reflected angle, similar to the reflection of light.

Significant diffraction occurs when the gap or obstacle is about the same size as the wavelength of the wave, causing the wave to spread out.

The speed of water waves decreases as they enter shallow water due to increased interaction with the bottom surface, which slows the wave down.

The unit of frequency is Hertz (Hz), which represents the number of cycles per second.

The relationship between frequency \( f \) and time period \( T \) is given by \( f = \frac{1}{T} \). Frequency is the reciprocal of the time period.

Wavelength is defined as the distance between two successive crests or troughs in a wave.

The formula to calculate wave speed is \( v = f \times \lambda \), where \( v \) is the wave speed, \( f \) is the frequency, and \( \lambda \) is the wavelength.

The time period \( T \) of a wave is the reciprocal of its frequency \( f \). Given \( f = 2.5 \) Hz, the time period \( T = \frac{1}{2.5} = 0.4 \) seconds.

Wave speed \( v \) is calculated using the formula \( v = f \times \lambda \). Given \( f = 0.125 \) Hz and \( \lambda = 8.0 \) m, the speed \( v = 0.125 \times 8.0 = 1.0 \) m/s.

Periodic motion is a motion that repeats itself in equal time intervals, such as the swinging of a pendulum or the vibration of a guitar string.

In Simple Harmonic Motion (SHM), the acceleration of the object is directly proportional to its displacement but in the opposite direction, as described by Hooke's Law \( F = -kx \).

The direction of acceleration in SHM is always directed towards the mean position, acting as a restoring force that brings the object back to equilibrium.

The expression that represents the acceleration in SHM is \( a = -kx \), where \( k \) is the spring constant and \( x \) is the displacement from the mean position.

The mass of the bob does not affect the period of a simple pendulum. The period depends on the length of the string and the acceleration due to gravity.

The bob of a pendulum has maximum speed at the mean position during SHM, where the kinetic energy is at its maximum and potential energy is at its minimum.

The frequency \( f \) of a simple pendulum is the reciprocal of its period \( T \). Given \( T = 2.01 \) seconds, the frequency \( f = \frac{1}{2.01} \approx 0.50 \) Hz.

The net force on the bob at the mean position is zero because it is at the equilibrium point where the restoring force is balanced.

Shock absorbers in a car are a practical example of damped oscillation, where the oscillations gradually decrease due to the damping effect of the shock absorbers.

Damping in an oscillating system is caused by friction or other resistive forces that dissipate energy, leading to a gradual decrease in amplitude.

In a damped system, the amplitude of oscillation decreases gradually over time due to the loss of energy caused by damping forces.