Speed of a Wave

Introduction

A wave is an unsettling influence that movements from one finish of a medium to the next. While watching a sea wave move over the medium (seawater), the pinnacle of the wave might be seen making a trip starting with one spot then onto the next throughout some stretch of time. The peak supposedly covers an enormous region. The speed of an item connects with how rapidly it moves and is generally expressed as the distance voyaged partitioned by the excursion time. The distance went by a given point on the wave (like a peak) in a given time period is the speed on account of a wave.

A brief outline

When a wave reaches the end of one medium and confronts the presence of another, it is said to have encountered the end of that medium. A wave put into one end of a slinky, for example, will travel through the slinky until it reaches the other end and the presence of a second person’s hand. Reflection is one of the behaviours that waves exhibit towards the end of a medium. The person’s hand will reflect or bounce the wave. When a wave reflects, it remains within the medium and simply reverses its travel direction. The disturbance can be observed travelling back to the originating end of a slinky wave. A slinky wave that travels from the beginning to the end of a slinky has double the distance.

Important concepts

Speed of the wave

The distance a wave travels in a particular amount of time, like the number of metres it travels per second, is called wave speed. The wave speed is represented by the following equation:

Speed = Distance / time

The speed of an ocean wave is 3 metres per second if the crest travels 30 metres in 10 seconds. But on the other hand, if the crest of an ocean wave reaches a distance of 40 metres in 10 seconds, the wave’s speed is 4 metres per second. We can deduct from this that the quicker wave travels a greater distance in the same amount of time.

We occasionally come across instances where the wave encounters both the end of one medium and the presence of another medium. Let’s use the example of a slinky to better understand this. The wave that is injected into the slinky by one person will travel through the slinky until it reaches the end of the slinky and the presence of a second person’s hand. Reflection is one of the behaviours that waves exhibit towards the end of a medium. When a wave is reflected, it simply stays in the medium and reverses its direction of travel. The slinky wave has travelled twice as far.

The Medium’s Dependence

Most waves’ speed is determined by the medium in which they pass. Waves travel the fastest over solids and the slowest via gases in general. This is because, in solids, particles are closest together, whereas, in gases, they are farthest apart. The energy distribution takes longer to travel from one particle to another across the medium when the particles are farther apart.

The formula of Wave Speed

The Wave speed formula which comprises wavelength and frequency is written by:

v = f λ

Where,

v = Velocity of the wave

f = Frequency of the wave

λ = Wavelength

• The distance travelled by a wave in a particular length of time is referred to as wave speed. The number of metres it travels per second, for example.
• The equation for wave speed, which is related to wavelength and frequency, is:
• Wavelength x Frequency = Speed When the wavelength and frequency values are known, this equation can be used to calculate wave speed.
• If the speed and the other value are known, the equation for wave speed can be written to solve for wavelength or frequency.
• The speed of most waves is determined by the medium or materials in which they move. Waves travel the fastest through solids and the slowest via gases in general.

Wave Characteristics

The qualities of waves are as follows:

• Wavelength – The distance between identical locations in neighbouring cycles of crests as well as the trough of a wave is known as the wavelength. In addition, it is measured in metres.
• Period – A particle on a medium’s period is defined as the time it takes for it to complete one complete vibrational cycle. It is expressed in seconds or minutes as a unit of time.
• Frequency – The frequency of a wave is defined as the number of waves travelling through a given spot in a given amount of time. The frequency unit in S.I is hertz (Hz), which equals one wave per second.

Significance of speed of a wave in the IIT JEE exam

In JEE Main, the 12th syllabus has 60 percent weightage while the class 11th syllabus has 40 percent weightage, to put it another way. The class 11 waves chapter accounts for around 5% of the total. Every year, this subject is often quizzed on 4 to 5 questions. It will not only make it easier for you to understand the concepts, but it will also aid in their retention for a longer period.

Also read: Kirchhoff’s Laws and their Applications

FAQs

What is the definition of a wave?

A wave is a type of disruption that occurs in moving material. Waves in the water, for example, flow across a medium and can be seen moving from one place to another. It can also be defined as an object's motion in terms of speed, which represents the object's velocity.

What is the significance of wave speed?

Light moves a million times faster than sound waves; hence wave speed is significant. The speed of a wave is important because it determines how quickly the energy it contains is transmitted from one location to another.

What are the different types of wave speed?

The speed of a wave varies on the medium. The type of wave and the physical features of the medium where it travels can both influence it. Electromagnetic waves are an exception since they may move through a vacuum. When a wave passes through most substances, the material will vibrate according to Hooke's law, and the speed will not be affected by frequency. Linear waves are electromagnetic waves that flow in a vacuum or in a linear medium and have a constant speed.