What Is a Travelling Wave? Complete Guide with Diagrams
Have you ever sat by a lake and observed the waves created on the surface of the water when you throw a stone into it? This is a good visual example of the propagation of waves and makes it simpler for you to understand travelling of waves and all other concepts related to it. Our universe has an amazing way of informing us about any changes in the physical world. When there are changes the information about that disturbance moves gradually outwards. It moves far from the source of disturbance in all the directions. When the said information travels, it travels in the form of a wave, just like the way waves are created when you throw a stone in the still water. This is known as the travelling wave.
Define Travelling Wave
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Before understanding what is travelling wave, let’s understand waves. Wave can be defined as a disturbance in a medium that travels transferring momentum and energy without any actual movement of the medium. However, the medium must have elastic properties. In our everyday life, there are many examples of waves, for example, ocean waves, strings of musical instruments, etc. On the other hand, a travelling wave is a wave in which the positions of minimum and maximum amplitude travel through the medium.
Points To Remember
Here are some of the points that are necessary to keep in mind about the wave:
Every wave has a high point and a low point. The high points are known by the name of crests. On the other hand, the low points are named by troughs.
Amplitude is the maximum distance of the disturbance from the midpoint of the wave to either the top of the crest or the bottom of a trough.
The maximum distance between the two adjacent troughs or the two adjacent crests is known as a wavelength.
Now, the time period is actually the time taken to complete one vibration.
Frequency is the number of vibrations the wave undergoes in one second.
You can witness an inverse relationship between both frequency and time period. The relationship is given below,
T=1f
The speed of a wave is given by the travelling wave equation,
V=λf
Where 𝛌 is the wavelength.
What are the Various Types of Travelling Waves?
Each type of wave contains different characteristics. And with these characteristics, we can easily distinguish between them. Here is a list of different types of waves that have been categorized based upon their particle motion.
Pulse Waves - the sudden disturbance that travels through a medium is known as a pulse wave. The disturbance can be caused by a chain reaction or sudden compression of air caused by an explosion. One example of a pulse wave is thunder. It comprises only one crest that travels through the transmission medium.
Continuous Waves - it is an electromagnetic wave that has constant amplitude and frequency. It is a typical sine wave and is considered to be of infinite duration. It was used in the earlier days of radio transmission.
Transverse Waves - in the transverse wave, the movement of the particles is at right angles to the motion of the energy. It is generated through a solid object like a stretched rope. Trampoline is the best example to understand this wave.
Longitudinal Waves - in this type of travelling wave the motion of the wave-particle is in the same direction as the propagation of the wave. In simple words, the movement of the particles is parallel to the motion of the energy. The best example for longitudinal waves is sound waves moving through the air when you hear a loudspeaker playing in the distance.
There is a second way to characterize the waves by types of matter they are able to move or travel through.
Electromagnetic Waves - this type of wave can travel easily through a vacuum. It does not need any medium, soft or hard to travel. An example of an electromagnetic wave is mobile phone waves or sound waves. They don't need any vacuum to travel.
Physical waves - Unlike electromagnetic waves, they require a medium to travel. They are further distinguished on the basis of phases of matter through which they can move.
Longitudinal Waves - these waves can easily pass through liquids and games.
Transverse Waves - they require a solid material or medium to propagate.
Problems based on travelling wave equation
Solved Examples
1: A wave on a rope is shown on the right at some time t. What is the wavelength of this wave? If the said frequency is about 4 Hz, what will be the wave speed?
Solution:
Now, for all the periodic waves, you will find v = λ/T = λf.
Details of the calculation:
The wavelength λ is 3 m. The speed is v = λf = (3 m)(4/s) = 12 m/s.
FAQs on Travelling Wave in Physics: Concepts & Examples
1. What is a travelling wave?
A travelling wave, also known as a progressive wave, is a disturbance that moves from one point to another through a medium or space, transferring energy without the net movement of the medium itself. The particles of the medium oscillate about their fixed equilibrium positions as the wave passes through them.
2. What are the key characteristics that describe a travelling wave?
A travelling wave is described by several key characteristics:
- Amplitude (A): The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
- Wavelength (λ): The spatial period of the wave, representing the distance over which the wave's shape repeats.
- Frequency (f): The number of complete oscillations or cycles that occur per unit of time.
- Wave Speed (v): The speed at which the wave propagates through the medium. It is related to frequency and wavelength by the formula v = fλ.
- Time Period (T): The time taken for one complete oscillation. It is the reciprocal of frequency (T = 1/f).
3. What is the general mathematical equation for a one-dimensional travelling wave?
The displacement `y` of a particle in a one-dimensional sinusoidal travelling wave can be described by the function: y(x, t) = A sin(kx - ωt + φ). In this equation, `A` is the amplitude, `k` is the angular wave number (2π/λ), `ω` is the angular frequency (2πf), `x` is the position, `t` is the time, and `φ` is the phase constant.
4. How is a travelling wave different from a standing wave?
A travelling wave and a standing wave differ in several fundamental ways. A travelling wave transports energy from one point to another, and all its particles oscillate with the same amplitude. In contrast, a standing wave does not transport energy; it is confined within a region. In a standing wave, the amplitude of oscillation varies with position, being zero at points called nodes and maximum at points called antinodes.
5. What actually moves forward in a travelling wave if the particles of the medium only oscillate?
This is a key concept in wave mechanics. While the individual particles of the medium (like water molecules or sections of a rope) only oscillate around their fixed equilibrium positions, it is the disturbance itself that propagates. This disturbance carries energy and momentum forward through the medium. So, what travels is not matter, but the pattern of motion and the energy associated with it.
6. What are some common real-world examples of travelling waves?
Travelling waves are abundant in the physical world. Some common examples include:
- Ripples on a pond: When a stone is dropped into water, the disturbance travels outwards as circular waves.
- Sound waves: The sound from a speaker travels through the air as a pressure wave to reach your ears.
- Light waves: Electromagnetic waves from the Sun travel through the vacuum of space to reach Earth.
- Waves on a string: If you flick one end of a stretched rope, a wave pulse travels down its length.
7. What factors determine the speed of a travelling wave through a medium?
A common misconception is that the source of the wave determines its speed. However, the speed of a travelling wave is determined solely by the properties of the medium through which it propagates. For example, the speed of a wave on a string depends on the string's tension and linear mass density. Similarly, the speed of a sound wave in air depends on the air's temperature, pressure, and density, not on how loud the sound is.
8. How do the signs in the wave equation y(x,t) = f(kx ± ωt) indicate the direction of wave propagation?
The relative sign between the spatial term (kx) and the temporal term (ωt) in the wave function directly indicates the direction of travel along the x-axis. A negative sign, as in (kx - ωt), signifies that the wave is propagating in the positive x-direction. Conversely, a positive sign, as in (kx + ωt), signifies that the wave is propagating in the negative x-direction.
