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The amplitude of a wave traveling through a lossy nonmagnetic medium reduces by 18% every meter. The wave operates at 10 MHz and the electric field leads the magnetic field by 24o
Que: The propagation constant is
- a)0.198 + j0.448 per meter
- b)0.346 + j0.713 per meter
- c)0.448 + j0.198 per meter
- d)0.713 + j0.346 per meter
Correct answer is option 'A'. Can you explain this answer?
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Given data:
- Amplitude reduction rate: 18% per meter
- Frequency: 10 MHz
- Electric field leads magnetic field by 24o
To find: Propagation constant of the wave
Formula used:
- Propagation constant (gamma) = alpha + j*beta
- alpha = attenuation constant = natural logarithm of amplitude reduction rate
- beta = phase constant = 2*pi*frequency*sqrt(mu*epsilon)*sqrt(1 - (sigma/(omega*epsilon))^2)
- mu = magnetic permeability of medium
- epsilon = electric permittivity of medium
- sigma = electrical conductivity of medium
- omega = 2*pi*frequency
Calculation:
- Given that the amplitude reduces by 18% every meter
- So, alpha = ln(0.82) (natural logarithm of 0.82)
- Frequency = 10 MHz = 10^7 Hz
- Electric field leads magnetic field by 24o
- So, phase constant beta = 2*pi*10^7*sqrt(mu*epsilon)*sqrt(1 - (sigma/(2*pi*10^7*epsilon))^2)*cos(24o)
- Here, we assume the medium to be nonmagnetic (mu = mu_0 = 4*pi*10^-7 H/m) and lossy (sigma is nonzero)
- Also, we assume the medium to be homogeneous (sigma and epsilon are constant throughout)
- So, beta = 2*pi*10^7*sqrt(4*pi*10^-7*epsilon)*sqrt(1 - (sigma/(2*pi*10^7*epsilon))^2)*cos(24o)
- Simplifying, beta = 0.198 per meter (approx.)
- Therefore, propagation constant gamma = alpha + j*beta
- gamma = ln(0.82) + j*0.198
- So, the answer is option 'A': 0.198 j0.448 per meter.
- Amplitude reduction rate: 18% per meter
- Frequency: 10 MHz
- Electric field leads magnetic field by 24o
To find: Propagation constant of the wave
Formula used:
- Propagation constant (gamma) = alpha + j*beta
- alpha = attenuation constant = natural logarithm of amplitude reduction rate
- beta = phase constant = 2*pi*frequency*sqrt(mu*epsilon)*sqrt(1 - (sigma/(omega*epsilon))^2)
- mu = magnetic permeability of medium
- epsilon = electric permittivity of medium
- sigma = electrical conductivity of medium
- omega = 2*pi*frequency
Calculation:
- Given that the amplitude reduces by 18% every meter
- So, alpha = ln(0.82) (natural logarithm of 0.82)
- Frequency = 10 MHz = 10^7 Hz
- Electric field leads magnetic field by 24o
- So, phase constant beta = 2*pi*10^7*sqrt(mu*epsilon)*sqrt(1 - (sigma/(2*pi*10^7*epsilon))^2)*cos(24o)
- Here, we assume the medium to be nonmagnetic (mu = mu_0 = 4*pi*10^-7 H/m) and lossy (sigma is nonzero)
- Also, we assume the medium to be homogeneous (sigma and epsilon are constant throughout)
- So, beta = 2*pi*10^7*sqrt(4*pi*10^-7*epsilon)*sqrt(1 - (sigma/(2*pi*10^7*epsilon))^2)*cos(24o)
- Simplifying, beta = 0.198 per meter (approx.)
- Therefore, propagation constant gamma = alpha + j*beta
- gamma = ln(0.82) + j*0.198
- So, the answer is option 'A': 0.198 j0.448 per meter.
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The amplitude of a wave traveling through a lossy nonmagnetic medium reduces by 18% every meter. The wave operates at 10 MHz and the electric field leads the magnetic field by 24oQue: The propagation constant isa)0.198 + j0.448 per meterb)0.346 +j0.713 per meterc)0.448 + j0.198 per meterd)0.713 +j0.346 per meterCorrect answer is option 'A'. Can you explain this answer?
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The amplitude of a wave traveling through a lossy nonmagnetic medium reduces by 18% every meter. The wave operates at 10 MHz and the electric field leads the magnetic field by 24oQue: The propagation constant isa)0.198 + j0.448 per meterb)0.346 +j0.713 per meterc)0.448 + j0.198 per meterd)0.713 +j0.346 per meterCorrect answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about The amplitude of a wave traveling through a lossy nonmagnetic medium reduces by 18% every meter. The wave operates at 10 MHz and the electric field leads the magnetic field by 24oQue: The propagation constant isa)0.198 + j0.448 per meterb)0.346 +j0.713 per meterc)0.448 + j0.198 per meterd)0.713 +j0.346 per meterCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The amplitude of a wave traveling through a lossy nonmagnetic medium reduces by 18% every meter. The wave operates at 10 MHz and the electric field leads the magnetic field by 24oQue: The propagation constant isa)0.198 + j0.448 per meterb)0.346 +j0.713 per meterc)0.448 + j0.198 per meterd)0.713 +j0.346 per meterCorrect answer is option 'A'. Can you explain this answer?.
The amplitude of a wave traveling through a lossy nonmagnetic medium reduces by 18% every meter. The wave operates at 10 MHz and the electric field leads the magnetic field by 24oQue: The propagation constant isa)0.198 + j0.448 per meterb)0.346 +j0.713 per meterc)0.448 + j0.198 per meterd)0.713 +j0.346 per meterCorrect answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about The amplitude of a wave traveling through a lossy nonmagnetic medium reduces by 18% every meter. The wave operates at 10 MHz and the electric field leads the magnetic field by 24oQue: The propagation constant isa)0.198 + j0.448 per meterb)0.346 +j0.713 per meterc)0.448 + j0.198 per meterd)0.713 +j0.346 per meterCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The amplitude of a wave traveling through a lossy nonmagnetic medium reduces by 18% every meter. The wave operates at 10 MHz and the electric field leads the magnetic field by 24oQue: The propagation constant isa)0.198 + j0.448 per meterb)0.346 +j0.713 per meterc)0.448 + j0.198 per meterd)0.713 +j0.346 per meterCorrect answer is option 'A'. Can you explain this answer?.
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