Oscillations and Waves Physics Notes Problems and Solutions

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Oscillations and Waves

A wave is a dynamic disturbance (change from equilibrium) of one or more quantities in physics, mathematics, and related subjects, usually described by a wave equation. At least two field quantities in a wave medium are involved in physical waves. Periodic waves occur when variables periodically oscillate around an equilibrium (rest) value at a specific frequency.

Examples include water waves, sound and light

Waves have the following characteristics

• Particles in a medium traveling through a wave vibrate only slightly about their average positions, but they are not permanently displaced in the direction of wave propagation.
• Along or perpendicular to the line of wave travel, each subsequent medium particle exhibits the same motion as the one before it.
• During wave motion, only the energy is transferred, but not the part of the medium.

Types of waves

There are two basic types, longitudinal and transverse. Transverse waves are on the water, traveling up and down the surface, and longitudinal waves, similar to sound, have alternating compression and rarefaction in the medium. The highest point of a transverse wave is called the crest, and the lowest point is called the trough.

The distance between the successive peaks or troughs of the wave is called wavelength, and wave height is called amplitude. How many crests or troughs pass a particular point in a unit of time is called frequency. Wave speed can be expressed as wavelength multiplied by frequency.

Longitudinal waves

Particle displacement in a longitudinal wave is parallel to the direction of wave propagation. For example, a One-dimensional longitudinal plane wave propagating in a tube. The particles don’t move down the tube with the wave; They oscillate back and forth about their equilibrium positions. Select a particle and watch its movement. The wave appears as a movement of a compressed region, which moves from left to right.

Examples:

• Sound waves
• Ultrasound waves
• Seismic P-waves

We can remember the movement of particles in longitudinal waves using the ‘P’ sound: longitudinal waves such as seismic P-waves can be thought of as stress or push waves when they move parallel to the waves.

Compression and rarefaction of Longitudinal waves:

• Compressions are high pressures caused by the proximity of particles
• Rarefactions are areas of low pressure because particles spread apart

Transverse waves

When the particles of the medium move at right angles to the direction of wave propagation, the wave is called transverse. For waves, there is a net displacement of the wave, but there is no net displacement of the particles of the medium. Thus there are two different motions: the motion of the particles of the medium and the motion of the wave.

Examples:

• Ripples on the water’s surface
• Vibrations in a guitar string
• Mexican wave at the sports stadium
• Electromagnetic waves – example: light waves, microwaves, radio waves
• Seismic S-waves

What are oscillations in waves?

A wave is said to oscillate, meaning to move back and forth in a regular, repetitive manner. These fluctuations may be between extremes of position, force or size. Different types of waves have different types of oscillations. Longitudinal waves: Oscillation is parallel to the direction of the wave.

What are Oscillations and Waves

Oscillations and waves are two significant phenomena discussed in physics. The concepts of oscillations and waves are widely used in many fields and are essential to understanding the world.

Rocking and swaying in a hammock are the most basic examples of oscillation. If you think critically, you will realize that in both of these examples, the motion is repetitive, and the swing or swing goes back and forth about a certain point. Another example is a pendulum wall clock, in which the pendulum periodically repeats its movement. When several objects move together and undergo oscillatory motion, they form a wave.

To understand the previous statement, consider the disturbance created in a pond when you drop a stone into still water. The disturbance (wave) appears to move outward in a circular pattern. But if you put the cork on the disturbance, you will see that the cork does not move out. It just swings where you put it. The disturbance is a waveform in which energy is transferred from one particle to another instead of an actual physical transfer.

Essential points about Oscillations and Waves:

Oscillatory motion is a particular type of periodic motion. But in this motion, the object moves back and forth to an average position over time. It is essential to understand that every oscillatory motion is periodic motion, but not every periodic motion is oscillatory. For example, the Earth’s rotation around the Sun is periodic but not oscillatory.

Some basic terms related to oscillatory motion:

Period of Time: The shortest period of time over which the motion starts to repeat itself is called the period of time. It is denoted by T.

Frequency refers to the number of movement repetitions per unit of time. In simple words, it is the reciprocal of the time period. It is denoted by f.

Periodic Function – A function expressed by the superposition of sine and cosine functions of different periods and appropriate coefficients.

Amplitude is a positive constant representing a particle’s maximum displacement in two directions. It is denoted by A.

Phase constant – The phase constant is the initial position/phase of the particle in SHM.

Conclusion:

Oscillation is the periodic motion of a particle or system that causes a wave. A wave is created either mechanically or electromagnetically by oscillation. Waves can also cause oscillation. Oscillation is a phenomenon localized to a particular region, whereas a wave is a traveling phenomenon.