STANDING WAVE ON A STRING

The standing wave patterns are also anti nodal. areas – areas that correspond to the back and forth vibration area between the top slide upwards and the slope downward slope. Antinodes are found in areas close to the area where two disturbing waves are constantly disturbed constructively. Static wave patterns are always reflected in the alternating pattern of nodes and antinodes.

There are a variety of patterns that can be produced to vibrate within a thread, slinky, or thread. Each pattern corresponds to the vibrations that occur in certain frequencies and are known as harmonic. The lowest frequency at which a bullet unit can vibrate to form a standing wave pattern is known as the base frequency or initial harmonic.

THEORY

Standing Waves

Standing waves are identified by nodes and antinodes. Particle vibration amplitude is high in antinodes and minimum in nodes. Vibration inside the cord can produce a variety of patterns. Each pattern corresponds to a vibration that occurs at specific frequencies and is called a harmonic. The lowest frequency at which a rope vibrates to form a standing wave is called the primary frequency or first harmonic. Wavelength and wave speed determine the frequency of each harmonic.

Standing wave on Endless Length string

Let us consider two harmonic waves of the same amplitude and period T and wavelength λ that move at the same speed in the opposite direction.

y1 = Sin (kx – )t)

y2 = Sin (kx + wt)

Considering the principle of superposition the result can be calculated as

Result y = y1 + y2

= Sin (kx – ωt) + Sin (kx + wt)

y = 2Asin (kx) cos ()t)

The figure represents SHM for particle collection. Here the word 2ASin (kx) is the size of the resulting wave. From the amplitude expression, it can be concluded that the height of the particles that make up SHM depends on the location of the particles.

Nodes

The wave magnitude is zero in all kx values ​​giving sin kx = 0. It means kx = 0, π, 2π ….. nπ the vibration of the particle will be zero. Here n is the whole number.

By entering k = 2π / λ we get

(2π / λ) x = nπ

⇒ x = nλ / 2

Therefore, x = 0, λ / 2, λ, 3λ / 2 …… ..

These zero-shift points in the particles are called nodes.

Antinodes

The amplitude will have a maximum value of 2A for all kx values ​​giving sin kx = ± 1. This means kx = π / 2, 3π / 2 ——— (n + ½) π the vibration of particles. it will be high.

By entering k = 2n + 1π / λ we get

(2π / λ) x = (2n + 1) π / 2

⇒ x = (2n + 1) λ / 4

⇒ x = λ / 4, λ, 3λ / 4,5λ / 4 …… ..

These points at which the particle release is highest are called antinodes. The nodes and antinodes in a standing wave are evenly spaced, the distance equal to λ / 2, where λ / wavelength.

Waves on a string with Two Fixed Ends

Consider the same L-length cord extended between two unchanging ends. The wave that travels to one side of the rope shows at the end and then reversed due to the fixed ends. These two identical waves travel in the opposite direction forming a vertical wave. The length of the cable is given as L so the wavelength of the wave is limited by the boundary condition.

λ = 2L / n, here n = 1,2,3… ..

Standing waves are formed on the rope only if the wavelength satisfies the L-relationship. If the v is the speed at which the waves travel through the rope, then the frequency of the wave

f = v / λ = nv / 2L, n = 1,2,3… ..

Notes are built at fixed limits. In addition to the nodes, if an antinode is present in the middle of the thread, the stretched cord is said to vibrate at the basic frequencies. The lowest resonance frequency corresponding to n = 1 is the basic frequency. High frequencies are called harmonics. Harmonics is a double standard.

Standing Wave Stone with One Fixed Limit

If the thread has one of its fixed ends and the other end is free, the node will be built at the fixed end and the antinode will be built at the free end. A simple stop wave created in this case is a quarter of the wavelength. The next possible stop wave will be created by adding both node and antinode. The wavelength will be three-quarters of the wavelength. Generally, wavelengths can be labeled

λ = 4L / n, here n = 1,2,3… ..

Then the frequency of the dry wave is blocked

f = nv / 4L

Features of standing waves

Stagnant waves are motionless. Disruption does not go anywhere.

Standing waves with zero amplitude points called nodes and high amplitude points are called antinodes.

There will be no flow of power in any medium.

The distance between two consecutive nodes or antinodes is equal to λ / 2, and the distance between the antinode and the nearest node is λ / 4.

The pressure change is high in the node and the minimum in the antinodes.

The medium is divided into a number of segments. All the particles in a particular phase will vibrate in stages. However, the amplitude increases from zero upwards between the node and the antinode. Particles in neighboring phases vibrate in opposite phases.

The rotation time of any central particle is the same as that of the partial waves.

CONCLUSION

Standing waves are produced on the rope when equal waves travel in a different direction. When the right conditions are met, the distortion between the moving waves causes the cord to move up and down in segments, as shown below. This segment of vibration does not give the appearance of movement in the unit length. This practice is called standing wave or vertical wave and is accompanied by an audible vibration of the cord.