DEFINATIONS:
1.Superconductivity: Superconductivity is the ability of certain materials to conduct a direct electric current (DC) with practically zero resistance.
2.Critical temperature: The temperature at which a material’s electrical resistivity drops to absolute zero is called the critical temperature or transition temperature Tc.
3.Critical magnetic effect: The critical magnetic field of a superconductor is a function of temperature. The variation of Hc with temperature is given by Hc=Ho[1-(T/Tc)²].
Where Ho is the critical field at T=0k. the critical field decreases with the increasing temperature and becoming zero at T=Tc.
4.Meissner effect: The complete expulsion of all the magnetic field by a superconducting material is called the Meissner effect.
5. Acoustics: Acoustic is the science of sound which deals with the properties of sound waves, their origin, propagation and their action on obstacles.
6. Reverberation time: Reverberation time is the persistence or prolongation of sound in a hall even after the source stopped emitting sound.
7. Musical sound: Musical sound is a type of sound characterized by specific pitches, timbres, and rhythms that are organized in a meaningful and aesthetically pleasing way. It is produced by instruments or voices and has a distinct musical quality that distinguishes it from other types of sound.
8. Noise: The unwanted sound is called a noise, The hall or room should be properly insulated external and internal noises.
9. Pitch: Pitch is the subjective perception of a sound’s frequency, determining its highness or lowness, and is measured in hertz.
10. Loudness: The uniform distribution of loudness in a hall or a room is an important factor for satisfactory hearing. Sometimes, the loudness may get reduced due to excess of sound-absorbing materials used inside a hall or room.
11. Timbre: Timbre is the unique quality of a sound that distinguishes it from other sounds of the same pitch and loudness, determined by the combination of harmonics and overtones present in the sound wave.
12. Absorption coefficient ‘a’: The absorption coefficient ‘a’ represents the fraction of sound absorbed by a material or surface, and is expressed as a decimal or percentage value.
13. Intensity level: Intensity level is a measure of the loudness of sound waves, expressed in decibels, that compares the sound wave intensity to a reference level.
14. Ultrasonics: Ultrasonics refers to the study and application of high-frequency sound waves, typically above the range of human hearing, for various purposes such as imaging, cleaning, and measurement.
15. Magnetostriction effect: Magnetostriction is a phenomenon in which a material undergoes a change in shape or size when it is subjected to a magnetic field.
16. Piezoelectric effect: When pressure is applied to one pair of opposite faces of crystals like quartz, tourmaline, Rochelle salt, etc. cut with their faces perpendicular to its optic axis, equal and opposite charges appear across its other face. This phenomenon is known as Piezoelectric effect.
17. SONAR: SONAR stands for Sound Navigation and Ranging. It is a technology that uses sound waves to detect and locate objects underwater.
QUESTIONS:
Que 1: What do you mean by the Superconductivity phenomenon? Explain by plotting Electrical resistivity vs temperature for a superconductor and a normal metal.
Ans: Superconductivity is a phenomenon where certain materials exhibit zero electrical resistance and perfect diamagnetism when cooled below a certain critical temperature. This critical temperature, also known as the transition temperature, varies for different materials and can range from a few degrees above absolute zero to several hundred degrees Celsius.
In contrast, normal metals have a finite electrical resistance that decreases with temperature but never reaches zero, as shown in the following graph:
Normal metal resistivity vs temperature
On the other hand, superconductors show a sharp drop in resistivity at the critical temperature, as shown in the following graph:
Superconductor resistivity vs temperature
The sudden drop in resistivity is known as the Meissner effect, which results in the expulsion of magnetic fields from the superconductor. This behavior is due to the formation of Cooper pairs, which are pairs of electrons that are strongly bound together and move through the material with zero resistance.
Que 2: What are the properties of superconductors? Discuss in detail with necessary Diagram/formula.
Ans: (i)Electrical resistance : The electrical resistance of a superconducting material is very low and is of the order of 10-7 Ω m.
(ii) Effect of impurities : When impurities are added to superconducting elements, the superconducting property is not lost, but the T value is lowered.
(iii) Effect of pressure and stress : Certain materials are found to exhibit the superconductivity phenomena on increasing over them. For example, cesium is found to exhibit superconductivity phenomena at Tc = 1.5K on the pressure applying a pressure of 110 Kbar. In superconductors, the increase in stress results in increase of the Tc value.
(iv) Isotope effects : The critical or transition temperature Tc value of a superconductor is found to vary with its isotopic mass. This variation in Tc ,with its isotopic mass is called the isotopic effect.
The relation between Tc , and the isotopic mass is given by
Tc∝1/√M
i.e., the transition temperature is inversely proportional to the square root of the isotopic mass of a single superconductor.
(v) Magnetic field effect : If a sufficiently strong magnetic field is applied to a superconductor at any temperature below its critical temperature Tc , the superconductor is found to undergo a transition from the superconducting State to the normal state.
This minimum magnetic field required to destroy the superconducting state is called theCritical magnetic field Hc. The critical magnetic field of a superconductor is a function of temperature. The variation of Hc with temperature is given by
Hc = Ho[1-(T/Tc)2] ———–(1)
Where Ho , is the critical field at T = 0k. The critical field decreases with increasing temperature and coming zero at T = Tc .
Figure
Critical current density Jc and critical current Ic .
Que 3: Explain with a diagram, the Meissner effect phenomenon showing the effect on Superconductors in the presence and absence of magnetic field.
Ans: The complete expulsion of all the magnetic field by a superconducting material is called the ‘Meissner effect’.
When a superconducting material is placed in a magnetic field (H>H) at room temperature the magnetic field is found to penetrate normally throughout the material (Figure 5.3(a)).
However, if the temperature is lowered below T, and with H<H, the material is found to reject all the magnetic field penetrating through it, as shown in Figure 5.3(b).
The above process occurs due to the development of surface current, which in turn results in the Development of magnetization M within the superconducting material. Hence, as the developed magnitation and the applied field are equal in magnitude but opposite in direction, they cancel each other everywhere inside the material. Thus, below T, a superconductor is a perfectly diamagnetic substance (χm = -1).
The Meissner effect is a distinct characteristic of a superconductor from a normal perfect Conductor. In addition, this effect is exhibited by the superconducting materials only when the applied Field is less than the critical field Hc.
Que 4: Show that the Magnetic Susceptibility of a superconductor is negative.
Ans: We know that for a magnetic material the magnetic induction or magnetic flux density B is given by
B = µₒ(M+H) ———–1.
Where µₒ = permeability of free space ; M = intensity of magnetization ; H = applied magnetic field.
But, we know that for a superconductor B=0
Therefore, equation 1 can be written as
0 = µₒ (M + H)
µₒ ≠ 0
M + H = 0
M = -H
M/H = -1
Hence for superconductor magnetic susceptibility is negative and maximum.
Que 5:What is Critical temperature Tc, Critical current density Jc, Critical magnetic field Hc? Discuss the relation between them with necessary diagram.
Ans: Critical temperature Tc: This is the temperature below which a superconductor exhibits zero electrical resistance and perfect diamagnetism.
Critical current density Jc: This is the maximum current density that a superconductor can carry without losing its superconducting properties.
Critical magnetic field Hc: This is the maximum magnetic field that a superconductor can withstand without losing its superconducting properties.
The relationship between Tc, Jc, and Hc is shown in the following diagram:
The diagram shows the superconducting region (shaded area) in a Tc vs. H plot for a superconductor. As the temperature increases, the critical current density decreases and the critical magnetic field increases. At Tc, both Jc and Hc become zero, and the material becomes a normal conductor.
Que 6: Differentiate between Type-I and Type-II superconductors.
Ans:
| Type-I superconductors. | Type-II superconductors. |
| 1. These superconductors are called as soft superconductors. | 1.These superconductors are called as hard superconductors |
| 2. Only one critical field exists for these superconductors. | 2.Two critical fields H c1 (lower critical field) and H c2 (upper critical field) exist for these superconductors |
| 3. The critical field value is very low. | 3.The critical field value is very high. |
| 4. These superconductors exhibit perfect and complete Meissner effect. | 4.These do not exhibit a perfect and complete Meissner effect. |
| 5. These materials have limited technical applications because of very low field strength value. Examples: Pb, Hg, Zn, etc. | 5.These materials have wider technological applications because of very high field strength value. Examples: Nb,Ge, Nb,SiY,Ba₂Cu,O7. etc. |
Que 7: Discuss the characteristics of Musical Sound.
Ans: 1.Pitch-Related to frequency of sound.
2.Loudness-Related to intensity of sound
3.Timbre-Related to quality of sound.
Pitch: This refers to the perceived highness or lowness of a sound and is determined by the frequency of the sound waves. In music, pitch is used to create melody and harmony.
Timbre: This is the unique quality of a sound that allows us to distinguish between different instruments or voices. Timbre is determined by the harmonic content of the sound wave and the way it changes over time. It is what gives a guitar a different sound than a piano, for example.
Loudness: Loudness is a characteristic which is common to all sounds, whether classified as musical sound or noise,
Loudness is a degree of sensation produced on ear. Thus, loudness varies from one listener to another. Loudness depends upon intensity and also upon the sensitiveness of the ear. Loudness and intensity are related to each other by the relation
L = K log10I
Where K is a constant.
From this relation it is seen that loudness is directly proportional to the logarithm of intensity, and is known as Weber-Fechner law.
dL/dI =K/I
Que 8: What is intensity? Explain with formula.
Ans: Intensity I of sound wave at a point is defined as the amount of sound energy flowing per unit area in unit time when the surface is held normal to the direction of the propagation of sound wave.
i.e, 1 = Q/(At)
Therefore, if A = 1m2 and t = 1 sec, then l = 0 where Q is sound energy The intensity is a physical quantity which depends upon factors like amplitude a, frequency f velocity v of sound together with the density of the medium ρ.
Therefore, the intensity I in a medium is given by
The unit of intensity is Wm-2
I = 2𝜋2f2a2
The minimum sound intensity which a human ear can sense is called the threshold intensity. Its value is 1012 watt/m2. If the intensity is less than this value then our ear cannot hear the sound
This minimum intensity is also known as zero or standard intensity The intensity sound is measured with reference to the standard intensity.
Que 9: What are the factors affecting acoustics of buildings? Explain with their remedies?
Ans: The various factors affecting the acoustics of buildings such as reverberation time, loudness, focuss echo, echelon effect, resonance and noise.
(1) Reverberation
Reverberation is the persistence or prolongation of sound in a hall even after the sour stopped emitting sound.The reverberation time is the time taken by the sound to fall below the minimum audibility level In order to have a good acoustic effect.
Remedies:
By providing windows and openings.By having full capacity of audience in the hall or room.By using heavy curtains with folds.By covering the floor with carpets.By decorating the walls with beautiful pictures, maps, etc.
2) Loudness
The uniform distribution of loudness in a hall or a room is an important factor for satisfactory hearing.
Remedies:
By using suitable absorbents at places where noise is high. As a result, the distribution of loudness may become uniform.
3) Focusing and Interference Effect
The presence of any concave surface or any other curved surface in the hall or room may make the sound to be concentrated at this focus region. These regions are referred to as dead space. Hence, such surfaces must be avoided.
Remedy:
Curved surfaces can be avoided. If curved surfaces are present, they should be covered with suitable sound-absorbing materials.
4) Echo
An echo is heard due to the reflection of sound from a distant sound-reflecting object.
Remedy:
An echo can be avoided by covering long-distance walls and high ceilings with suitable sound-absorbing material. This prevents the reflection of sound.
5) Echelon Effect
It refers to the generation of a new separate sound due to multiple echoes.
Remedy:
The remedy to avoid the echelon effect is to cover such surfaces with sound-absorbing materials.
6) Resonance
Resonance occurs due to the matching of frequency.
Remedy:
The resonance may be avoided by fixing the window panels properly.
7) Noise
The hall or room should be properly insulated from external and internal noises.
Que 10: Explain the construction and working principle of Magnetostriction method for the Production of ultrasound using necessary diagram.
Ans: The Magnetostriction method for the production of ultrasound involves using the principle of magnetostriction, which is the property of certain materials to change their shape when subjected to a magnetic field.
Construction:
The basic components of a magnetostriction ultrasound generator include a magnetostrictive material, an electromagnet, and a transducer.
The magnetostrictive material is typically made of nickel or an alloy of nickel and iron, and is shaped into a rod or a wire.
The electromagnet is wound around the magnetostrictive material and is used to generate a magnetic field when a current is passed through it.
The transducer is attached to the magnetostrictive material and converts the mechanical vibrations produced by the material into ultrasound waves.
Working principle:
When a current is passed through the electromagnet, a magnetic field is generated which causes the magnetostrictive material to change its shape.
This change in shape results in the material vibrating at a high frequency, producing mechanical vibrations.
The transducer attached to the magnetostrictive material converts these mechanical vibrations into ultrasound waves.
By varying the frequency of the current passed through the electromagnet, the frequency of the ultrasound waves produced can be controlled.
Que 11: Explain the construction and working principle of Piezo electric method for the Production of ultrasound using necessary diagram.
Ans: The piezoelectric method is one of the most commonly used methods for the production of ultrasound. This method uses a piezoelectric crystal to produce high-frequency sound waves, which are then emitted into the medium through which the crystal is placed.
Diagram:
Construction:
The piezoelectric crystal used for this method is typically made of materials such as quartz, barium titanate, or lead zirconate titanate. The crystal is cut into a specific shape, usually cylindrical or disc-shaped, and has two electrodes attached to its surface.
Working Principle:
When an alternating voltage is applied to the electrodes, the piezoelectric crystal undergoes mechanical deformation due to the piezoelectric effect. The piezoelectric effect is the ability of certain materials to generate an electric charge in response to applied mechanical stress or pressure.
In the piezoelectric method for ultrasound production, the alternating voltage applied to the crystal causes it to vibrate at a high frequency, typically in the range of 1 to 10 MHz.
The sound waves produced by the piezoelectric crystal can be focused into a beam using an acoustic lens or mirror. This allows for precise targeting of the ultrasound energy to a specific location in the body for diagnostic or therapeutic purposes.
Que 12: How to find ocean depth using SONAR technique? Explain in detail with necessary Diagram.
Ans:
SONAR stands for Sound Navigation And Ranging, and it is a technique that uses sound waves to detect and locate objects underwater.
- Generate Sound Waves: First, a SONAR system generates a sound wave, typically in the form of a brief pulse of high-frequency sound. This sound wave is usually generated by an underwater speaker called a transducer.
- Transmit Sound Waves: The sound wave travels through the water and interacts with any objects in its path. When the wave encounters the ocean floor, it bounces back and returns to the transducer.
- Receive Echoes: The transducer then receives the echoes of the sound wave that bounced back. These echoes are converted into electrical signals, which are sent to a computer for analysis.
- Analyze Echoes: The computer analyzes the time it took for the sound wave to travel from the transducer to the ocean floor and back. This time is directly proportional to the distance traveled, which is twice the depth of the water.
- Calculate Depth: Using this information, the computer can calculate the depth of the water at the location where the sound wave was transmitted.
Que 13: Discuss the various important applications of Ultrasonic waves.
Ans: Medical Imaging: Ultrasonic waves are used in medical imaging to produce images of internal organs and tissues. This technique, called ultrasound, is non-invasive and does not use ionizing radiation. It is used for prenatal imaging, diagnosing diseases, and guiding medical procedures.
Non-destructive Testing: Ultrasonic waves are used for non-destructive testing in industries such as aerospace, automotive, and construction. They can detect flaws, cracks, and corrosion in metal parts without causing any damage, thus saving time and money.
Cleaning: Ultrasonic waves are used for cleaning delicate and complex parts such as electronic components, jewelry, and surgical instruments. The high-frequency sound waves create tiny bubbles in the cleaning solution, which implode and remove dirt and contaminants from the surface.
Welding: Ultrasonic welding is a technique used to join two plastic parts together using high-frequency vibrations. The parts are pressed together and heated by the vibrations, which melt the plastic and create a bond.
Distance Measurement: Ultrasonic waves are used for distance measurement in various applications such as level sensing, object detection, and robotics. A sensor emits a sound wave, which bounces off an object and returns to the sensor. By measuring the time it took for the sound wave to travel, the distance to the object can be calculated.
NUMERICALS:
Que 1: The critical temperature of Nb is 9.15 K. At zero kelvin, the critical field is 0.196 T. Calculate the critical field at 6 K.
Ans: Critical temperature of Nb (Tc) =9.15K , T= 6K
Critical field (H0 ) = 0.196 T , Hc = ?
Hc = H0 [1-[T/Tc]2]
= 0.1960[1-[6/9.15]2]
= 0.1960[1-0.4299]
Hc = 0.1117 T
Que 2: Calculate the critical current through a long thin superconducting wire of radius 0.5 mm. The critical magnetic field is 7.2 kA/m.
Ans: Given, Hc = 7.2 * 103 A/m , r = 0.5*10-3 m
Ic = 2𝜋rHc
= 2*3.14*0.5*10-3 *7.2 * 103
Ic = 22.608 A
Que 3: A source of sound has a frequency of 426 Hz and an amplitude of 0.65 x 10-2 m. Calculate the flow of energy across 1 m per second if the velocity of sound in air is 340 ms –1 and the density of air is 1.29 kg/m3 .
Ans: Given, frequency of sound (f) =426 Hz , Amplitude (a)=0.65*10-2 m ,
A= 1m2 , density of air (ρ) = 1.29 kg/m3 , velocity of sound in air(v) = 340ms-1
I = 2𝜋2f2a2
= 2*(3.14)2*(426)2*(0.65*10-2 )2* 1.29*340
I = 6.631*104 Wm-2
Que 4: A hall of volume 1000 m3 has a sound absorbing surface of area 400 m2. If the average absorption coefficient of the hall is 0.2, what is the reverberation time of the hall?
Ans: Given, hall of volume(V) = 1000 m3 , surface of area(S) = 400 m2 ,
average absorption coefficient of the hall (a) = 0.2 ,
reverberation time of the hall (T) = ?
T = 0.167V / aS = 0.167*1000/(0.2*400)
= 2.0875 sec
Que 5: A cinema hall has a volume of 7500 m3 . What should be the total absorption in the hall if the reverberation time is 1.5 seconds is to be maintained?
Ans: Given, cinema hall has a volume (V) = 7500 m3
Time (T) =1.5 sec , Σas = ?
T = 0.167V \Σas
Σas = 0.167 * 7500/1.5
= 835 sabine-m3