Visualising

Wave motion is an essential branch of physics and is a phenomenon that can be observed in everything on this earth. In this article, we could see the vital study material of visualising waves on the string. Wave on a string is a type of mechanical wave. Usually, mechanical waves need a medium to travel, for example, light waves and sound waves. These waves originate from the disturbance in the medium and the disturbance propagated through the medium. In this article, we could see the important study material notes of visualising waves on the string and the linear wave equation. In this visualising waves study notes, we cover the concept of wavelength, frequency, speed, power and intensity.

Visualising Wave

Wave on the String is a type of mechanical wave. Usually, mechanical waves need a medium to travel, like sound waves. These waves originate from the disturbance in the medium and the disturbance propagated through the medium.

Types of mechanical waves

The mechanical waves are classified based on the medium’s physical properties, such as

• Number of dimensions
• The shape of wavefronts
• Periodicity
• The direction of particle motion

Speed, wavelength, frequency of the string wave

If the wave source makes vibrations with a constant time period, the wave frequency(f) will be equal to the source frequency.

When the source completes one vibration, the disturbance distributes out the surface and one wave will get generated. When the source keeps vibrating with constant frequency f, the wave is produced with constant frequency. This holds for all the wave motions.

The linear wave equation

We can describe the motion of any point on the string by using the wave function y = A sin (t – kx + ). The point on the string moves vertically and x remains constant.

Find the transverse Velocity(Vy)

Find the transverse acceleration (Ay)

This is the linear wave equation of the travelling mode, developed from a sinusoidal mechanical wave travelling the medium. It is also known as a differential equation, which describes the wave on the string.

The speed of a wave on a string is expressed as below

= T/

 T – tension (unit –  N)

is the mass per length of the string (in kg/m)

The speed of v and tension T are corresponding values at that point when the tension is nonuniform.

The principle of superposition

Consider two waves travelling at the same time along a similar extended string in inverse ways. We can see pictures of waveforms in the string at every moment of time. It is seen that the net relocation of any component of the string at a given time is the mathematical amount of the removals because of each wave.

The string is stretched too far, but the individual displacements are not added to give the resultant displacement. This takes place in nonlinear waves.

This principle is also expressed when overlapping waves are algebraically added to form a resultant wave. Overlapping waves do not alter the travel of each other. 

Amplitude of reflected and transmitted waves

Let v1 and v2 be the speeds of the incident wave and reflected wave in mediums, then

Power transmitted along the string by a sine wave

When a travelling wave is established on a string, energy is transmitted along the direction of propagation of the wave in the form of potential and kinetic energy.

Energy transferred in one time period = Pav t = energy stored in one wavelength.

Intensity

The intensity of the wave is given by the power transferred per second per unit cross-sectional area

Intensity = Power / Cross-sectional area

= P/s

Conclusion

In this article, We have seen the study material notes of visualising waves on the string. We have also gone through important concepts like the linear wave equation and power transmitted along the string by a sine wave. Along with this, there are many laws of transverse vibrations of a string in the sonometer wire.