Speed of Travelling Waves

Almost every material and object on the planet has elastic binding forces. These elastic forces begin to act when the body is compressed or released, and the motion of one part of the system affects other parts. Thus, the motion of one part of the system affects the other parts of the system as well, resulting in a disturbance that travels through the entire system as a wave. When pebbles are thrown into water, for example, waves are created that travel in all directions. The goal here is to study and better understand these travelling waves.

What are Travelling Waves?

A travelling wave in a medium is a disturbance that propagates through it in a specific direction and at a specific velocity. A “disturbance” is typically defined as a displacement of the medium’s constituent parts away from their rest or equilibrium position. The idea here is to think of each part of an elastic medium as a potential oscillator that couples to neighbouring parts by pushing or pulling on them. When a travelling wave reaches a specific location in the medium, it causes that part of the medium to move by imparting energy and momentum to it.

Speed = Wavelength x Wave Frequency

In this equation, wavelength is measured in meters and frequency is measured in hertz (Hz), or number of waves per second. Wavelength and frequency is different for different mediums, so the speed of the respective waves will be different.

What are Waves?

Waves are actual disturbances that move without actual matter transfer. These waves carry energy, and the pattern of disturbance contains information that spreads from one location to another. All of our daily communications, such as phone signals and the internet, are actually waves of information that travel through various mediums to reach the users. These waves can be divided into two categories based on how they propagate –

Transverse Waves – The particles in the medium oscillate perpendicular to the wave’s motion.

Longitudinal Waves – The particles of the medium oscillate along the wave’s propagation direction.

Factors Affecting The speed of Sound in Gases

The Effect of Wind Direction: The speed of sound increases or decreases depending on the direction of the wind. When wind blows in the direction of sound propagation, the speed of sound increases; when wind blows in the opposite direction, the speed of sound decreases.

Temperature Effect: As the temperature of a gas rises, so does the speed of sound in the gas. where T is the gas’s temperature in kelvins.

Density Effect: The speed of sound is inversely proportional to the square root of the gas’s density.

Humidity has an effect on the speed of sound in air, which increases as humidity in the air increases. 

Velocity of a Wave

Because the particles of the medium oscillate to and fro in the wave, these waves can be mathematically described in terms of trigonometric functions similar to simple harmonic motions (SHM). For simplicity, the wave is assumed to be a transverse wave, so that if the position of the medium’s constituents is denoted by x, the displacement from the equilibrium position is denoted by y.

What is the Standing Wave Pattern?

It is possible, however, for a wave to be confined to a specific space in a medium and still produce a regular wave pattern that is easily discernible amidst the medium’s motion. For example, if an elastic rope is held end-to-end and vibrated at just the right frequency, a wave pattern with the shape of a sine wave is produced and seen to change over time. The wave pattern appears only when one end of the rope is vibrated at precisely the right frequency. When the proper frequency is used, the interference of the incident and reflected waves occurs in such a way that specific points along the medium appear to be stationary.

The observed wave pattern is often referred to as a standing wave pattern because it is characterised by points that appear to be stationary.

Mechanical Waves

Mechanical waves share characteristics with all other types of waves, including amplitude, wavelength, period, frequency, and energy. A small set of underlying principles can describe all wave characteristics.

The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be modelled using a sine and cosine function combination. Consider the simplified surface water wave shown here, which moves across the water’s surface. In contrast to complex ocean waves, the medium, in this case water, moves vertically, oscillating up and down, while the wave’s disturbance moves horizontally through the medium.

Conclusion

When a travelling wave reaches a specific location in the medium, it causes that part of the medium to move by imparting energy and momentum to it. The speed of sound increases or decreases depending on the direction of the wind. When wind blows in the direction of sound propagation, the speed of sound increases; when wind blows in the opposite direction, the speed of sound decreases. As the temperature of a gas rises, so does the speed of sound in the gas. Where T is the gas’s temperature in kelvins. The speed of sound is inversely proportional to the square root of the gas’s density. Because the particles of the medium oscillate to and fro in the wave.