Reflection of sound waves

A bell ringing rapidly, a drum moving up and down to the beat and a reverse rating harp string are all examples of objects that make sounds.
In this article let us learn about the reflection of sound waves.

Learning reflection of sound waves

Have you ever shouted into a well or inside an empty hall or in a cave? One can hear their own voice after a short time. Why is it happenning ? It happens because the sound of your voice is reflected from the walls.
We can also try this by shouting  into a well or by the side of a steep hill. This phenomenon of hearing your own sound again is called an echo. The rolling of thunder is largely due to successive reflections from clouds and land surfaces. For the reflection of sound waves, we need an extended surface, or obstacle of large size which need not necessarily smooth or polished.

Learning reflection of sound waves from one medium to other:

Generally, when sound waves in one medium strike a large object of another medium such as air, a wall, etc… , a part of the sound is reflected, and the remainder is sent into the new medium. The speed of the sound in the two mediums and the densities of the medium help to determine the amount of reflection. If the sound travels at about the same speed in both the materials and both have about the same density, little sound will be reflected, instead most of the sound will be transmitted into the new medium. If the speed differs greatly in the two and their densities are greatly different, most of the sound will be reflected.
When you shout at a brick wall most of the sound is reflected, because brick is denser than air.

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Check my best blog Sinusoidal wave equation.

Sinusoidal wave equation

We found that the disturbance (whether pulse or wave, transverse or longitudinal) depends on both position x and time t. If we call the displacement y, we can write y = f(x,t) or y(x,t) to represent this functional dependence on time and position. In the example of the transverse pulse traveling along a Slinky as pictured in Fig. 17-2,

y(x,t) represents the transverse (vertical) displacement of the Slinky rings from their equilibrium position at given position x and time t. (Alternatively, in the longitudinal wave on the Slinky shown in Fig. 17-1, y(x,t) could represent the number of Slinky coils per centimeter at a given x and t.)
We can completely describe any wave or pulse that does not change shape over time and travels at a constant velocity using the relation y = f(x,t), in which y is the displacement as a function/of the time t and the position x. In general, a wave can have any shape so long as it is not too sharp. The trick then is to find the correct expression for the function, f(x,t).

Fortunately, it turns out that any shape pulse or wave can be constructed by adding up different sinusoidal oscillations. This makes the description of sinusoidal waves especially useful. So, for the rest of this section we'll discuss the properties and descriptions of continuous waves produced by displacing a stretched string using a sinusoidal motion like that shown in Fig. 17-3b. We will start by using the equation we developed in Chapter 16 to describe for sinusoidal motion at the location of a single piece of string. As we did in looking through the slit in Fig. 17-5, we will only let time vary. Next we can consider how to describe a snapshot that records the displacement of many pieces of the string at a single time. Finally, we can combine our snapshot with the results of peeking through a slit to get a single equation that ought to describe the propagation of a single sinusoidal wave. Basically we are trying to describe the displacement y of every piece of the string from its equilibrium point at every time. We are looking for y(x,t).

Looking Through a Slit: Sinusoidal Wave Displacement at x = 0
If we choose a coordinate system so that x = 0 m at the left end of the string in Fig. 17-3b, then the motion at the left end of the string can be described using Eq. 16-5 with the string displacement from equilibrium represented by y(x,t) = y(0,r) rather than by simply y(t). To simplify our consideration we assume that the initial phase of the string oscillation at x = 0 m and t = 0 s is zero. This gives us

where the angular frequency can be related to the period of oscillation by to = 2irlT. Although we use the cosine function in Chapter 16 to describe simple harmonic motion, it is customary to use the sine function to describe wave motion. As we mentioned in Chapter 16, when a sine function is shifted to the left by v/2 it looks like a cosine function. So we can also describe the same string displacement as a function of time at x = 0 m as

Note that using the sine function requires a different, nonzero initial phase angle given by ir!2. If we locate our slit at another nonzero value of x as shown in Fig. 17-5, then the initial phase (at t = 0 s) will often turn out to be different from w/2. In fact this initial phase is a function of the location x of the piece of string we are considering.
A Snapshot: Sinusoidal Wave Displacement at t = 0

Imagine that the man has been moving the end of the string up and down as shown in Fig. 17-36 for a long time using a sinusoidal motion. Instead of looking through a slit as time varies, we take a snapshot of the string at a time t = Os similar to that shown in Fig. 17-36. Then we expect our snapshot to be described by the equation

where A: is a constant and the "initial" phase when x is zero must also be tt!2. Note that if the snapshot of the string were taken at another time, the initial phase would probably be different.

Combining Expressions for x and t
Equation 17-1 describes the displacement at all times for just the piece of string located at x = 0 m. Equation 17-2 describes the displacement of all the pieces of string at t = Os. We can make an intelligent guess that the equation describing y(x,t) is some combination of these two expressions given by
y(x,t) = Ysin[(foc ± cot) + tt/2)], (17-3)

where tt/2 represents the initial phase when x = 0 m and t - 0 s for the special case we considered. 

In general we can describe the motion of our sinusoidal wave with an arbitrary initial phase by modifying Eq. 17-3 to get
 y(x,t) = Ysin[(fct ± tot) + 4>q)] (sinusoidal wave motion, arbitrary initial phase), (17-4)
where <f>₀ is the initial phase (or phase constant) when both x = Om and t = Os. The ± sign refers to the direction of motion of the wave as we shall see in Section 17-5. In cases where the initial phase is not important, we can simplify Eq. 17-3 by choosing an initial time and origin of the x axis that lies along the line of motion of the wave so that <t>o = 0 rad.

Atomic number 28

Introduction :
d – block elements are also called transition elements. Transition metals are those elements which contain partially filled d- sub shells either in their atoms or in their common oxidation states. Nickel is a silvery white metal and takes a high polish. Nickel is hard malleable, ductile, ferromagnetic and fair conductor of heat and electricity. Atomic number 28 belongs to Iron – cobalt group. 'Ni' is commercially obtained from pentlandite and pyrrholite of the subdury region of Ontario.
Characteristics of Atomic number 28:

• The element in the periodic table which has atomic number 28 is Nickel. 
• 'Ni' has mass number 58.6934. 
• 'Ni' has oxidation state of 2 and 3. 
• Atomic number 28 has electronic configuration [Ar]4s²,3d⁸. 
• Nickel has chemical formula ‘Ni’.
• Atomic number 28 belong to Period 4 and Group 10.
• 'Ni' belongs to d - block elements. 

Properties of atomic number 28:

• Oxidation states of 'Ni': The elements exhibit variable oxidation states depending on the number of electrons participating in the bonding. Ni has oxidation states 2 and 3. 
• Colors of transition metal ions:  When the visible light of wavelength 400 to 700 nm is passed through a solution of a transition metal compound, it absorbs a particular frequency of radiation and transmits the remaining colors.
• Magnetic properties of 'Ni':  The paramagnetic behavior is highly pronounced in case of iron, cobalt and nickel. Hence they are called ferromagnetic substances.
• Formation of complexes by 'Ni': These metal ions have a great tendency to combine with a large number of molecules or ions called ligands and form complexes. The bond between a metal ion and a ligand is coordinate. Hence, complex compounds are also known as coordination compounds.
• Chemical reaction: Nickel carbonyl can be oxidized, Chlorine oxidizes nickel carbonyl into NiCl₂, releasing carbon monoxide gas.

               2Ni(CO)₄  +  2ClCH₂CH=CH₂    ====>  Ni₂(μ-Cl)₂ (η³-C₃H₅)₂  +  8CO

• Catalytic properties of transition metals: Many transition metals and their compounds are used as catalysts in several inorganic and organic chemical reactions. Nickel catalyst is used in the hydrogenation of oils.                                                                                       Oils +  H₂    →  Fats
• Isotopes of Nickel: ⁵⁸Ni, ⁶⁰Ni, ⁶¹Ni, ⁶²Ni and ⁶⁴Ni are five stable isotopes of Nickel. ⁵⁸Ni being the most abundant.  ⁶²Ni is one of the most stable nuclides.
• Reaction of 'Ni' with halogens:

             Ni_(s)    +    cl_2(g)   ====>    NiCl_2(s)     (Yellow)
             Ni_(s)    +    Br_(g)    ====>    NiBr_2(s)     (Yellow)
             Ni_(s)    +    I_2(g)     ====>    NiI_2(s)       (black)

• Reaction of Nickel with acids:

             Ni_(s)     +   H₂SO_4(aq)  ====>  Ni²⁺_(aq)  +  SO^2-_(aq)  +  H_2(g)  

• Reaction of Nickel with air:

    Nickel metal does not react with air under normal condition. Finely divided Nickel metal readily reacts with air. At higher temperatures, the reaction appears not to proceed to completion but give some nickel(ll) oxide.
            2Ni_{(s)    +}    O_2(g)    ====>  2NiO_(s)                                                                                        

Uses of Atomic number 28:

• It is used in many industrial and consumer products, including stainless steel, magnets, coins, rechargeable batteries, electric guitar strings and special alloys. 
• 'Ni' is used in plating and as a green tint in glass. 
• Atomic number 28 is a metal alloy and its chief use in the nickel steels and nickel cast iron. 
• 'Ni' is widely used in many alloys, such as nickel brasses and nickel bronze. etc.
• Raney Nickel, a finely divided form of metal is alloyed with aluminum which absorbs hydrogen gas. 

Isotopes of carbon

Introduction to Carbon:
The element with atomic number 6 in the periodic table refers to Carbon which belongs to group 14.  This element is widely distributed in most of the planets.  Carbon is a nonmetallic and tetravalent element and it forms covalent bonds.  The common oxidation states of carbon are +4 in organic compounds and +2 in carbon monoxide and transition metal complexes.  Diamond is the hardest material of carbon where as ceraphite is the softest material.   Mainly there are three allotropes of carbon fullerenes, diamond and graphite and some other forms are ionsdaleite, buckminsterfullerene and also carbon nanotube.
Allotropic forms of element with atomic number 6:
Fullerene                                 
     

Isotopes of carbon:

Among seven isotopes carbon has two stable isotopes. Those two isotopes of carbon are carbon-14 which is a naturally occurring radioisotope, it is used in carbon dating. Carbon- 13 which forms only 1.07%. Carbon-8 is the shortest lived isotope. Carbon-19 is the isotope which exhibits nuclear halo.
Compounds of carbon:
In atmosphere, carbon is found in combination with other elements like oxygen, hydrogen etc.  For ex: carbon dioxide, carbon monoxide, carbon disulfide, carbon tetra fluoride, chloroform, carbon tetrachloride, methane, ethylene, acetylene , benzene , acetic acid its derivatives.
Organic compound containing carbon (carbon tetra fluoride):

Properties of carbon:

• Atomic mass: 12
• Appearance: solid
• Electronic configuration: 1s² 2s² 2p² or [He] 2s² 2p²
• Density: 1.8-3.5g/cm³
• Melting point: 3915K
• Oxidation states: +4, +2
• Vander walls radius: 170pm

Applications of carbon:
1. Without carbon life could not exist because it plays an important role.
2. Carbon-14 which is naturally occurring isotope is used in carbon dating.
3. Allotrope of carbon (graphite) is used in pencil leads.
4. Hydrocarbons in combination with carbon are used in the production of gasoline and kerosene.
5. In nuclear reactors, it is used as neutron moderator.
6. It is (charcoal) used in artwork as a drawing material.
7. Cellulose is a natural carbon containing polymer used in maintaining the structure of plants.
8. Synthetic carbon is used in the production of plastics
9. It is used in diamond industries.

10. Now a day’s used in the production of carbon nanotube.

Atomic structure of Iron

Introduction 
There is a need at all levels of the study of science to present the correct picture of any substance. Here is an attempt to present the correct picture of the Iron atom, which is best described in terms of its orbital structure and orientation.
Occurrence: Iron is one of the more common elements on Earth. It makes up about 5% of the Earth's crust. Most of this iron is found in various Iron oxides, such as the minerals; Hematite, Magnetite, and Taconite. The earth’s core consists largely of a metallic iron-nickel alloy. Although rare, these are the major form of natural metallic iron on the earth's surface.

Atomic structure of Iron

The atomic number of Iron element is 26, which indicates the presence of 26 protons and 26 electrons in its atom.
Naturally occurring Iron consists of four isotopes:
a) 5.845% of radioactive ⁵⁴Fe (half-life: >3.1×10²² years) Number of neutrons, n = 28.
b) 91.754% of stable ⁵⁶Fe, n = 30.
c) 2.119% of stable ⁵⁷Fe, n = 31.
d) 0.282% of stable ⁵⁸Fe, n = 32.
E) ^{6 0}Fe is an extinct radionuclide. n = 34.
Nucleus:
The nucleus of Iron (Fe) atom is made of 26 protons and 30 neutrons (is most abundant).  The total number of electrons in Iron atom is 26, which is equal to that of protons, which maintains the neutrality of the atom.   But, Iron has got two stable oxidation states, +2 and +3.
Electron distribution:
The ground state electronic configuration of Iron atom is given by:
  (1s²)    (2s²2s⁶)    (3s²3p⁶3d⁶)    (4s²)

As it is seen in the electronic configuration, there are four shells available in the Iron atom.
The first energy level - K shell (n=1) - consists of 2 electrons in s-orbital, spherical in shape.
The second energy level - L shell (n=2) - consists of 8 electrons, out of which 2 in s-orbital and 6 in p-orbital (dumb bell in shape).
The third energy level - M shell (n=3) - consists of 14 electrons, out of which 2 in s-orbital and 6 in p-orbital (dumb bell in shape) and 6 in d-orbital (double dumb bell in shape).
The fourth energy level - N shell (n=1) - consists of 2 electrons in s-orbital.
Whenever Iron is oxidized, the electrons are removed from the outermost shell.  An octet electronic configuration is attained when +3 state is reached, which is half filled d-orbital state. So, Fe⁺³ is most stable state of Iron.
 (1s²)    (2s²2s⁶)    (3s²3p⁶3d⁵)    (4s⁰)
Iron is more stable, when it is oxidized.  So, it has a very high tendency to liberate electrons and get converted into Ferric ion, which is reasonable by its atomic structure. This is the reason why Iron gets rust.

Significance of atomic structure

The knowledge of the atomic structure is very useful in describing the chemical as well as physical properties associated with the element. Precisely, it can be said that the secrete of life is hidden in the atomic structure.

Atomic number 27

Introduction :
The word ‘atomic number 27’ refers to Cobalt which is having the atomic number 27. The number of protons in a nucleus determines the identity of the atom is called as ‘atomic number’.  It is represented by the letter Z. For example a hydrogen atom contains one proton, so the atomic number of hydrogen is one (Z=1) similarly the atomic number of cobalt is 27 (Z=27).
Swedish chemist Georg Brandt (1694–1768) is credited with discovering cobalt (atomic number 27) circa 1735. The word cobalt (atomic number 27) is derived from the German kobalt, from kobold meaning "goblin", a term used for theory of cobalt (atomic number 27) by miners.
Occurrence:
Cobalt (atomic number 27) occurs in copper and nickel minerals and in combination with sulfur and arsenic in the sulfidic cobaltite minerals.

Method of Extraction:

1. Froth flotation process:
It is a process for selectively separating hydrophobic materials from hydrophilic. This is used in several processing industries.
Froth flotation process is based on the principle that the metallic sulphide particles of the ore are preferentially wetted by oil and gangue particles by water.

                                                                                                 Froth flotation process
In this process, the finely divided ore is added to a large amount of water contained in the tank. Certain oils like pine oil, eucalyptus oil etc, are added.  A current of compressed air is circulated through the water in the flotation tank. The metallic ore particles are preferentially wetted by the oil froth and rise to the surface along with the froth. The gangue material is wetted. Hence it settles at the bottom.
2. Roasting process:
It is a process in which the ores are heated to a high temperature below their melting point in the presence of excess of air. During this process, the moisture escape and the impurities like sulphur, arsenic, etc are oxidized to their volatile oxides. The messes become porous. It is generally carried out in a reverberatory furnace.
                        S +O₂ → SO₂↑
                         As  +  O₂  →  As₂O₃↑
       Sometimes, the sulphide ore are oxidized to sulphates
                   2ZnS + 3O₂ → 2ZnO + 2SO₂

     Roasting process

Applications of Cobalt (atomic number 27)::

• It is used in batteries.
• It is used as catalysts.     
• It is used as a pigment and coloring.
• It is used in a biological role.
• It is used for electroplating.
• It is used for electroplating due to its appearance, hardness, and resistance to oxidation.

Atomic and ionic radii

Introduction :

Atomic radii are also known as covalent radius.  Atomic radii describes the size of the atom of an element in its elementary state or in covalently linked molecule. It is measured in terms of picometers or Angstroms. It is the distance from the nucleus to the boundary of the surrounding cluster of electrons.

The bond length of a covalent linkage is the distance between the nuclei of the two bonded atoms. The bond length can be measured by X-diffraction method.

The internuclear distance between two unlike atoms in a covalent bond is the sum of the atomic radii of the two. For example, the covalent radii of hydrogen and chlorine are 0.037 nm and 0.099 nm respectively. Hence the internuclear distance in HCl molecule is 0.037 nm + 0.099 nm = 0.136 nm.

The atomic size will generally decrease from left to right in a period. This is because, when we proceed from one element another in a period, this results in a greater pull on electrons towards the nucleus. In a given period, the alkali metal atom of group 1A is the largest and the halogen atom in 7A is the smallest.

Ionic radii:

The ionic radii may be defined as the distance between the nucleus of an ion and the point up to which the nucleus has influence on its electron cloud.
The concept of ionic radii was developed independently by Victor Goldschmidt and Linus Pauling in 1920.
If ions in a crystal are regarded as spheres, the internuclear distance between two ions is equal to the sum of the radii of the ions. The internuclear distance is measured by X-ray analysis of ionic compounds. Knowing the radius of one ion, that of the other is calculated.
The interionic distance in potassium chloride crystal is 0.314 nm= r K⁺ + r Cl^- = 0.314 nm where r K⁺ and r Cl^- are the radii of potassium ion and chloride ion respectively. It is found that r K⁺ = 0.314 nm   Therefore r Cl^- = 0.314-0.133 = 0.181 nm.