Introduction to Speed of a wave

A wave is defined as the disturbance that travels along a channel or medium from one point to another. For example, waves of the ocean always travel along a medium/channel like sea’s water. Additionally, you will also notice that the wave crest moves from one location to other points at a given time interval, and we observe that the crest measures the distance covered by a wave. 

We commonly refer to an object’s speed as how quickly it is moving. We use the formula of distance covered per unit travel time to express it mathematically. For this topic, we will cover the concept of the speed of a wave with examples.

Definition of the Speed of a wave

A wave is a type of disturbance in a travelling medium. Here we will consider an example of ocean waves and water. We can define an object’s motion with respect to speed which is expressed as an object’s velocity. We visualize a wave at the time when a source is vibrating and disturbing a particle within a medium. This can be easily observed in the case of ripples in water when you drop a mass or a tuning fork.

However, sometimes a wave might move from one point to another across the medium. When a person introduces a wave from one location into slinky’s one end, it will move through it. Ultimately, it will get to the end portion of the slinky and the other person’s hand at the second location. 

One of the most significant behaviours of a wave is known as reflection towards the end of a medium.  The wave reflects on the hand of the person. When a wave goes through reflection, it stays within the medium. The wave hardly moves in the reversed travel direction. 

Here, the frequency of the wave is calculated by evaluating it as a number of waves/unit second. We use the reciprocated value of waves’ frequency to calculate the time period. Further, the distance measured between the corresponding locations for any two consecutive waves is defined as its wavelength. 

Hence, if the ocean wave’s crest is covering a distance of 20 m within a time period of 10 seconds, then we can calculate the speed of a wave as 2 m/s. Moreover, if the ocean wave’s crest travels a distance up to 25 m within 10 seconds, we will get the speed of the wave as 2.5 m/s.

Wave Speed Formula

The formula includes frequency and wavelength of the wave and is expressed as,

v = f × λ

Here,

v = Velocity of the wave

f = frequency of the wave 

λ = Wavelength

Speed = Wavelength x Frequency

Some solved examples of the speed of a wave

Q.1: If a light wave is travelling with the wavelength value of 300 nanometers, then calculate its frequency.

Sol: As given, 

Wavelength, λ = 300 nm,

Speed of light, v = 3 × 108 m/s.

The frequency is:

f = v/λ

f = (3 × 108) / (300 × 10-9)

= 1015 Hz

The frequency of the light wave is 1015 Hertz.

Q.2: If a sound wave in air has a wavelength of 6.88 millimeters, then calculate its frequency.

Sol: As Given,

Wavelength, λ = 1.5 mm,

Speed of sound, v = 344 m/s.

The frequency is:

f = v / λ

f = (344) / (6.88  × 10-3)

= 50 KHz

Here, sound waves’ frequency is 50 kHz.

Conclusion

1. Wave speed refers to the distance that the wave travels in a specific length of time. For instance, the amount of metres of the distance it travels per second.
2. Wave speed is linked to wave frequency and wavelength and is calculated by the equation: Speed = Wavelength x Frequency. The equation is utilised to calculate wave speed when the frequency and wavelength is given.
3. The equation of wave speed can be written in order to find the frequency wavelength when you know the other values and speed.
4. The speed of the majority of the waves is determined by the medium or material that they travel through. In general, waves travel the fastest through solid medium and the slowest through gas medium.