A wave is defined as a vibration that propagates through a medium, in the form of solids, liquids, and gases. Waves are vibrations that propagate. The ideal form of a wave will follow a sinusoidal motion in the form of repeated smooth oscillations.

In addition to electromagnetic radiation, waves are also present in the medium in which they can travel and can transfer energy from one place to another without causing the particles of the medium to move permanently; ie there is no mass transfer. Each special point oscillates around one particular position.

A thing is called a medium if:

- Linear if the different waves at all given points in the medium can be summed.
- Limited if it is finite, otherwise it is called infinite.
- Uniform if the physical characteristics do not change at different points.
- Isotropic if the physical properties are “same” in different directions.

In general, waves can be written mathematically with the equation:

A negative value (-) is used if the wave originates from the left of point P (the wave propagates to the right). A positive (+) value is used if the wave originates from the right of point P (the wave propagates to the left).

If the source of the wave has vibrated once, the wave has had some distance to propagate. Because there is a frequency of vibration every second, the equation for the speed of wave propagation is:

While the wave frequency equation is as follows:

Then the speed of the wave can be written by the equation:

### Wave Phase Angle

The phase angle of the wave is the angle that the object has traveled to reach the point P. The equation for the phase angle of the wave is written as follows.

### Phases and Phase Differences of Waves

The number of revolutions that have been made or the extent to which the point propagates is expressed by the phase. The wave phase equation is as follows.

While the phase difference is when there are two points on the rope, then the phase difference is the distance between the two points. The wave phase difference equation is as follows.

### Properties of Waves

To understand a wave, we need to know its properties first, as explained below:

#### Wave Dispersion

Wave dispersion is the change in the shape of a wave as it propagates through one medium. The medium through which the wave travels does not depend on the length or frequency of the wave is called a dispersive medium.

#### Wave Reflection

When a wave hits an obstacle or is at the end of its propagation medium, some of the wave will be reflected. The angle formed by the incident wave with respect to the reflected surface is equal to the angle made by the reflected wave, according to the law of reflection.

The incoming angle is described as the angle made by the incoming wave against the perpendicular line of the reflected surface. Meanwhile, the reflection angle is the angle at which the wave is formed that has been reflected. This law of reflection applies to all types of waves.

#### Wave Refraction

When a wave passes through two different mediums, some will be reflected while the other will be transmitted. The bending of a transmitted wave beam is known as refraction or refraction.

One example is when we put a pencil into a glass of water and the pencil looks as if it is broken.

#### Wave Interference

Wave interference or merging occurs when two coherent waves meet. Wave interference can be seen in the ripples of water on the surface. When there are two sources of waves on the surface of the water, the wavefronts will meet and form an interference pattern.

#### Wave Polarization

Polarization refers to the direction in which the wave vibrations can be absorbed. Wave polarization consists of vertical and horizontal polarization.

We can see the vertical polarization by moving the string from top to bottom. Meanwhile, we can observe the horizontal polarization by moving the string to the right and left.

#### Doppler Effect

If a wave source and its receiver are moving relative to each other, the frequency that the receiver detects is not the same as the source frequency.

When the two move closer to each other, the detected frequency will be greater than the source frequency. This phenomenon is known as the Doppler effect. The Doppler effect is used by police radar to measure the speed of a car.

### Wave Type

In reality the classification of waves is very diverse, some are according to the direction of propagation, the medium of propagation, according to the dimensions of the spread of propagation and others. However, what will be discussed this time is only two classifications of waves, namely according to the direction of propagation and the need for the medium for propagation.

#### 1. Waves according to the direction of propagation

The wave with the direction of interference is parallel to the direction of its propagation.

An example of a longitudinal wave is a sound wave, this sound wave is analogous to a longitudinal pulse in a vertical spring under tension made to oscillate up and down at an end, then a longitudinal wave travels along the spring, the coils in the spring vibrate back and forth in the direction in which the disturbance travels along the spring.

Transverse waves are waves with disturbances that are perpendicular to the direction of propagation. For example, light waves where electric waves and magnetic field waves are perpendicular to the direction of propagation.

#### 2. Waves according to the needs of the medium in propagation

Mechanical waves are waves that require a medium to propagate. Examples of wave mechanics on ropes, sound waves.

- Electromagnetic wave

Electromagnetic waves are waves whose energy and momentum are carried by an electric field (E) and a magnetic field (B) which can propagate through a vacuum or without the need for a medium in the wave propagation.

Source of electromagnetic waves:

- Electrical oscillation.
- Sunlight produces infrared rays.
- Mercury lamps produce ultra violet.
- Unstable atomic nuclei produce gamma rays.
- The bombardment of electrons in a vacuum tube on a metal chip produces X-rays (used for x-rays).

The relationship between the electric field (E) and the magnetic field (B) is expressed by Maxwell’s equations. Maxwell’s equations are the laws that underlie electromagnetic field theory.

Examples of electromagnetic waves are light waves, radio waves.

### Based on Amplitude

Based on the amplitude, waves are divided into two, namely traveling and stationary waves.

#### 1. Walking waves

A traveling wave is a wave that has a fixed amplitude. That is, every point through which the wave amplitude is always the same. An example of a traveling wave is a water wave.

#### 2. Stationary wave

Stationary waves are a combination of incident waves and reflected waves which have the same amplitude and frequency but the direction of propagation is opposite. The point that vibrates with the maximum amplitude is called the belly, while the point that vibrates with the minimum amplitude is called the node.

### Wave Magnitude

When discussing waves, there must be major quantities that must be understood. The quantities in question are as follows.

#### 1. Amplitudo (A)

Amplitude is the maximum deviation of the wave which has units of meters (m).

#### 2. Wavelength (λ)

If viewed from a transverse wave, the wavelength is the distance between two adjacent peaks or the distance between two adjacent valleys.

If viewed from a longitudinal wave, the wavelength is the distance between two adjacent joints or stretches.

#### 3. Wave frequency (f)

Frequency is the number of waves that can be formed each second. Mathematically, the frequency is formulated as follows.

Information:

f = wave frequency (Hz);

n = number of waves formed; and

t = wave travel time (s).

#### 4. Wave period (T)

Period is the time it takes a wave to travel one wavelength. Period can also be defined as the time it takes a wave to make one rotation.

Mathematically, the period is formulated as follows.

Information:

f = wave frequency (Hz);

T = periode (s);

n = number of waves formed; and

t = wave travel time (s).

#### 5. Fast wave propagation

The speed of propagation is the length of the distance traveled by the wave per unit time. Mathematically, the speed of wave propagation is formulated as follows.

Information:

f = wave frequency (Hz);

T = periode (s);

v = speed of wave propagation (m/s); m

λ = wavelength (m).

Wave (Freepik)

### Example of Wave Question

1. Ocean waves approaching the boat with a speed of 10 m/s. If the distance between two adjacent wave crests is 2 m, determine the period and frequency of the wave!

Discussion:

Is known:

v = 10 m / s

λ = 2 m

Asked: T and f =…?

Discussion:

Based on the formula for the speed of wave propagation, we get:

The frequency is formulated as follows.

So, the period and the period of the wave are 0.2 s and 5 Hz, respectively.

2. A traveling wave has the equation y = 0.01 sin (4t-x), x and y in cm and t in seconds. What is the magnitude of the deviation at a point 5 cm from the origin when the origin has been vibrating for 2 seconds?

Is known

y = 0.01 sin π (4t- x)

x = 5 cm

t = 2 s

The solution

y = 0.01 sin π (4 2- 5)

y = 0.01 sin π (8- 5)

y = 0

So the magnitude of the wave deviation is 0 where it indicates the wave is at the wave node point.

3. The following is the equation for the displacement of the traveling wave y = 5 sin (0.5 t – 10.5 x). The period of the wave is….

Is known

y = 5 sin π (0.5 t – 10.5 x)

The solution

ω = 2π / T

0.5 π = 2 π / T

T = 2/0.5

T = 4 s

So the period of the wave is 4 seconds.

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