## Introduction

First, we will understand the definition of a wave then we will move to wave speed. A wave is a disturbance that moves through a medium from one end to another end. It can be seen in the ocean water as an ocean wave moving along the medium. When we observe it carefully we can see that the crest of the wave is moving from one location to another over a given interval of time. This crest is observed to cover the distance. As we know that the speed of an object refers to how fast that object is moving and is usually expressed as the distance travelled per unit time of travel. We can also observe a wave when a source vibrates and disturbs a particle in the medium. It can usually be seen in the tuning fork or ripples in water when a body is dropped, etc. In this topic, we will discuss what wave speed is the formula with few solved examples.

## What is Wave Speed?

Wave speed is defined as the speed at which a wave travels. It is related to wavelength, frequency and period. It is given by the formula v=fλ

Where v is the velocity of the wave,

f is the frequency of the wave, and

λ is the wavelength.

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

Wave frequency is the number of waves that pass through a fixed point in a given amount of time. The most commonly used wave speed is the speed of visible light and an electromagnetic wave.

### The Speed of a Wave

The speed of a wave is defined as the distance a wave travels in a given amount of time. It is the number of meters it travels per second. Wave speed can be represented by the equation:

\[Speed=\frac{Distance}{Time}\]

### Properties of Waves

Following are the properties of waves:

Amplitude – Amplitude is the maximum height of the wave, usually measured in meters.

Wavelength – It is the distance between identical points in the adjacent cycles of crests as well as the trough of a wave. It is also measured in meters.

Period – It is defined as the time taken by a particle on a medium to make one complete vibrational cycle. It is measured in units of time such as seconds or minutes.

Frequency – The frequency of a wave is defined as the number of waves passing a point in a certain time. The S.I unit of frequency is hertz (Hz) which is equal to one wave per second.

The period can also be defined as the reciprocal of the frequency and vice versa.

\[Period=\frac{1}{Frequency}\]

Speed – The speed of a wave refers to the distance travelled by a given point on the wave (crest) in a given interval of time.

\[Speed=\frac{Distance}{Time}\]

### Speeds of Different Types of Waves

The speed of a wave is different in a different medium. It can be determined by the type of wave and the physical properties of the medium in which it travels. An exception is found in the electromagnetic waves as they can travel through a vacuum. For most substances, the material will vibrate that will obey a Hooke's law force as a wave passes through it and the speed will not depend on frequency. Electromagnetic waves in a vacuum and waves travelling through a linear medium are termed linear waves and they have a constant speed.

### Dependence Medium of the Wave Speed

The speed of most waves depends on the medium or the matter through which they travel. Usually, waves travel fastest in the solids and slowest in the gases. This is because particles are more close to each other in solids whereas farthest apart in gases. When the particles are farther apart, it takes a longer time for the energy distribution to pass from one particle to another through the medium.

### Solved Examples

1.A Light Wave Travels With a Wavelength of 500 nm. Determine its Frequency.

Sol: Given, wavelength λ = 500 nm

We know the velocity of light (v) = 3 x 10^{8} m/s^{2}

The frequency is calculated by formula,

\[f=\frac{v}{\lambda }\]

Now put the value of v and λ in the above formula

\[f=\frac{3 \times10^{8}}{500 \times10^{-9} }\]

\[f=\frac{3 \times10^{8}}{5 \times10^{-7} }\]

f = 6 x 10^{14} Hz

Hence the frequency of the light wave is 6 x 10^{14} Hz

2. Wavelength of a Sound Wave is 1.5 nm. Determine its Frequency.

Sol: Given wavelength λ = 1.5 nm

As we know the velocity of sound wave (v) = 343.2 m/s

Frequency is calculated by the formula

\[f=\frac{v}{\lambda }\]

Now put the value of wavelength and velocity in the formula,

\[f=\frac{343.2}{1.5 \times10^{-9} }\]

f = 22.8 KHz

Hence the frequency of the sound wave is 22.8 kHz

### Conclusion

Wave speed is the distance travelled by a wave travels in a given amount of time. For example the number of meters, it travels per second.

Wave speed is related to wavelength and wave frequency and it is given by the equation:

Speed = Wavelength x Frequency. This equation can be used to calculate wave speed when the wavelength and frequency value is known.

The equation for wave speed can be written to solve for wavelength or frequency if the speed and the other value are known.

The speed of most of the waves depends on the medium or the matter through which they travel. Generally, waves travel fastest through solids medium and slowest through gases medium.

1. What is a Wave?

Ans: A wave is a kind of disturbance in a moving medium. For example, waves of the ocean move in a medium and we can see the movement of the wave from one point to the other. It can also be described as the motion of an object regarding the speed which describes the velocity of the object.

2. What are the Different Types of Waves?

Ans: Different types of waves are:

(i) Transverse Waves

(ii) Longitudinal Wave

(iii) Electromagnetic Waves

(iv) Mechanical waves

(v) Matter Waves

(vi) Electromagnetic Waves

3. Why is Wave Speed Important?

Ans: Wave speed is important because light waves travel a million times faster than sound waves. We should know the speed of a wave because this is the speed at which the energy it carries is transferred from one place to another place.