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
$$T_{c}∝{1}{√M}$$
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
$$H_{c} = H_{o}[1-{(\frac{T}{T_{c}}})^{2}] \,———-(1)$$
Where Ho , is the critical field at T = 0k. The critical field decreases with increasing temperature and coming zero at T = Tc .
Figure 5.2 shows the variation of critical field Hc as a function of temperature. The material is aid to be in the superconducting state within the curve and is non-superconducting in the region outside the curve.
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>Hc) 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<Hc, 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.
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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
$$\frac{M}{H} = -1$$
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: Nb2Ge, Nb3Si ,Y1Ba₂Cu3O7. etc. |
Que 7: classify sound depending upon frequency? discuss classification of audible sound.
Ans: Sound can be classified based on its frequency, with the frequency range of audible sound being the focus of classification. Audible sound is the range of sound frequencies that can be detected by the human ear. This range typically spans from 20 Hz (hertz) to 20,000 Hz, although it can vary slightly from person to person, especially as individuals age. Here’s a classification of audible sound based on frequency:
- Infrasound (Below 20 Hz):
- Infrasound refers to sound waves with frequencies below the lower limit of human hearing (20 Hz). While humans can’t consciously perceive infrasound, some animals, such as elephants and whales, can detect and communicate using infrasound. Infrasound can also be generated by natural phenomena like earthquakes and volcanic eruptions.
- Audible Sound (20 Hz – 20,000 Hz):
- This is the range of sound frequencies that can be heard by the human ear. Audible sound is further divided into subcategories: a. Subsonic: Frequencies in the lower part of the audible range, typically from 20 Hz to around 100 Hz. Subsonic sounds can be felt as vibrations more than heard. b. Bass: Frequencies in the range of 100 Hz to about 250 Hz. These frequencies contribute to the lower, resonant tones in music and are important for creating a sense of depth and richness in audio. c. Midrange: Frequencies from around 250 Hz to 2,000 Hz. The midrange contains many of the fundamental frequencies of musical instruments and is crucial for speech intelligibility. d. Treble: Frequencies from 2,000 Hz to 20,000 Hz. Treble frequencies provide clarity and brightness to audio and are responsible for many high-pitched musical tones and the crispness of speech.
- Ultrasonic Sound (Above 20,000 Hz):
- Ultrasonic sound refers to sound waves with frequencies above the upper limit of human hearing (20,000 Hz). While humans cannot hear ultrasonic sounds, many animals, such as bats and dolphins, use ultrasonic echolocation for navigation and hunting. Ultrasonic sound also finds applications in various fields, including medical imaging, cleaning, and pest control.
- Hypersonic Sound (Above 1,000,000 Hz):
- Hypersonic sound includes extremely high-frequency sound waves that are well beyond the range of human and most animal hearing. It is often used in scientific research and industrial applications, such as materials testing and non-destructive testing.
- Megasonic Sound (Above 1,000,000,000 Hz):
- Megasonic sound refers to sound waves with frequencies in the gigahertz range. This ultra-high-frequency sound is employed in precision cleaning processes in industries like semiconductor manufacturing and optics.
Que 8 : 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 log10 I
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.
$$\frac{dL}{dI} =\frac{K}{I}$$
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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 10 : Explain the construction and working principle of Piezo electric method for the Production of ultrasound using necessary diagram.
Ans:
i) Inverse piezoelectric effect:
If an alternating voltage is applied to one pair of opposite faces of the crystal, alternatively mechanical
contractions and expansions are produced in the crystal and the crystal starts vibrating. This effect is
known as inverse piezoelectric effect or electrostriction effect.
When the frequency of the applied alternating voltage is equal to the vibrating frequency of the crystal, then the crystal will produce ultrasonic wave.
The experimental arrangement is shown in fig. Quartz crystal Q is placed between two metal plates A and B, connected to the coil L3. The coil L1, L2 and L3 is connected to triode valve. Coil L1 is connected
parallel with variable capacitor C1 forming the tank circuit. The high tension battery is connected between free end of L2 and the cathode of triode.
Working:
- When high tension battery is switched on, the oscillator produces high frequency alternating voltage given by
- The f of oscillation can be controlled by the variable capacitor C1.
- Due to the transformer action an emf is induced in the secondary coil L3. This emf are impressed on
the plates A and B , will excite the quartz crystal into vibrations. - By adjusting the variable capacitor C1, frequency can be achieved in resonant conditions and crystal will produce ultrasonic waves. The frequency of vibrations is
- Where, E is Young’s modulus, ρ is the density of the material, l is length.
Que 11 : 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.
$$V=\frac{OA+OB}{t}$$
$$Depth\,of\,sea=\frac{vt}{2}$$
Que 12 : 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.
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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 = ?
$$H_{c} = H_{o}[1-{(\frac{T}{T_{c}}})^{2}]$$
$$H_{c} = 0.1960[1-{(\frac{6}{9.15}})^{2}] $$
$$H_{c} = 0.1960[1-0.4299]$$
$$H_{c} = 0.1117 T$$
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
<!–Extra**–>
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 = 2𝜋2f2a2ρv
= 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) = ?
$$T = \frac{0.167V}{as}$$
$$T = \frac{0.167*1000}{(0.2*400)}$$
$$T = 2.0875 \,sec $$
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 = ?
$$T = \frac{0.167V}{Σas}$$
$$Σas = \frac{0.167 * 7500}{1.5}$$
$$ Σas = 835 \,sabine-m_{3} $$