Quick Formula for Complete Wave Dispersions with Examples and Solutions

YOGYAKARTA - Waves are one of the physical phenomena that are often encountered in daily life, ranging from sound, light, to water waves. In simple terms, waves can be understood as vibrations that propagate through a medium or even a vacuum.

The propagation velocity of a wave is a measure of how fast the energy in the wave moves from one point to another in a unit of time. To calculate it, an understanding of wavelength, frequency, and period is needed. All these quantities are interrelated and can be calculated using simple formulas.

However, before discussing the quick formula for the propagation of waves, it is good to first understand the types of waves and their characteristics.

Types of Waves and their Characteristics

Waves can be classified into two main types, namely transverse waves and longitudinal waves. Transverse waves occur when the direction of vibration is perpendicular to the direction of wave propagation, for example waves on a rope or water surface. While longitudinal waves are waves where the direction of vibration is parallel to the direction of propagation, such as sound waves in the air.

Each wave has an important magnitude that can be measured. The wavelength (λ) is the distance between two successive wave peaks, the frequency (f) is the number of vibrations per second, while the period (T) is the time it takes for one full vibration. The relationship between these three quantities is the basis for the formation of the wave speed formula.

Tools such as oscilloscopes or seismographs can be used to observewaves. However, in many cases, we can simply use mathematical equations tofind the value of the wave speed. This makes the concept of the wave speedformula practical to be applied in various fields.

Fast Formula for the Wave Dispersivity

In general, the wave speed is formulated as:

v = λ × f or v = λ / T

v = speed of the wave (m/s)

λ = wavelength (m)

f = frequency (Hz)

T = period (seconds)

This formula shows that the larger the frequency or wavelength, the faster thewave propagates. Conversely, if the period is large, then the speed of the wavewill be smaller. With this understanding, we can calculate various wavephenomena easily.

Examples of Fast-moving Wave Problems

A transverse wave has a wavelength of λ = 5 meters and a frequency of f = 10 Hz. What is the speed of the wave (v)?

Solution:

It is known that f = 10 Hz.

λ = 5 meters

Then the value of the substitution into the formula v= λ x f.

v=λx f

v = 5 m x 10 Hz = 50 m/s.

A wave has a period T = 0.5 second and a wavelength λ = 2 meters. What is thespeed of the wave (v)?

Solution:

It is known that T=0.5 s.

λ = 2 m

Then the value of the substitution into the formula v= λ / T.

v = λ / T

v = 2m/0.5s = 4m/s.

The speed of propagation of sound waves in air is 128 m/s. If the frequency is 64 Hz, what is the wavelength (λ)?

Solution:

It is known that v = 128 m/s.

f = 64 Hz

Then the substitution of the value into the formula λ=v/f. This formula is obtained from v=λ x f by moving λ to the left side.

λ = v/f

λ = 340m/s : 680Hz = 0.5m.

By understanding the basic concepts and their application in the example problems, students can more easily master the material about waves.

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