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For a telephone line, β= 0.02rad/km. If frequency is 1 kHz. Calculate time taken to travel 3.14 km by the wave in µs
Correct answer is '10'. Can you explain this answer?
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For a telephone line, β= 0.02rad/km. If frequency is 1 kHz. Calculate...
Given:
β = 0.02 rad/km (attenuation constant)
Frequency (f) = 1 kHz = 1000 Hz
Distance (d) = 3.14 km
To Find:
Time taken to travel 3.14 km by the wave in µs
Solution:
The attenuation constant β represents the rate at which the amplitude of the wave decreases as it travels through the medium. It is given by the formula:
β = 2πf/v
Where v is the velocity of propagation of the wave.
Step 1: Calculate the velocity of propagation (v)
v = 2πf/β
Step 2: Calculate the time taken to travel 3.14 km
Time (t) = d/v
Step 1: Calculate the velocity of propagation (v)
v = 2πf/β
= 2π(1000)/(0.02)
= 100π/0.02
= 5000π m/s
Step 2: Calculate the time taken to travel 3.14 km
Time (t) = d/v
= 3.14/(5000π)
= 3.14/(5000*3.14159)
≈ 0.02 ms
Converting milliseconds to microseconds:
1 ms = 1000 µs
Therefore, 0.02 ms = 0.02 * 1000 µs = 20 µs
Hence, the time taken for the wave to travel 3.14 km is approximately 20 µs.
Final Answer:
The time taken to travel 3.14 km by the wave is '20 µs'.
β = 0.02 rad/km (attenuation constant)
Frequency (f) = 1 kHz = 1000 Hz
Distance (d) = 3.14 km
To Find:
Time taken to travel 3.14 km by the wave in µs
Solution:
The attenuation constant β represents the rate at which the amplitude of the wave decreases as it travels through the medium. It is given by the formula:
β = 2πf/v
Where v is the velocity of propagation of the wave.
Step 1: Calculate the velocity of propagation (v)
v = 2πf/β
Step 2: Calculate the time taken to travel 3.14 km
Time (t) = d/v
Step 1: Calculate the velocity of propagation (v)
v = 2πf/β
= 2π(1000)/(0.02)
= 100π/0.02
= 5000π m/s
Step 2: Calculate the time taken to travel 3.14 km
Time (t) = d/v
= 3.14/(5000π)
= 3.14/(5000*3.14159)
≈ 0.02 ms
Converting milliseconds to microseconds:
1 ms = 1000 µs
Therefore, 0.02 ms = 0.02 * 1000 µs = 20 µs
Hence, the time taken for the wave to travel 3.14 km is approximately 20 µs.
Final Answer:
The time taken to travel 3.14 km by the wave is '20 µs'.
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Community Answer
For a telephone line, β= 0.02rad/km. If frequency is 1 kHz. Calculate...
Β = 0.02rad/km,f = 1kHz,d = 3.14km
Wavelength λ = 2π/β = 2π/0.02 = 314.159km
Velocity v = ω/β = 2πf/β = 2π∗1000/0.02 = 3.14 × 105km/sec
Time t = d/v = 3.14/(3.14 × 10∧5) = 10−5Sec
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For a telephone line, β= 0.02rad/km. If frequency is 1 kHz. Calculate time taken to travel 3.14 km by the wave in µsCorrect answer is '10'. Can you explain this answer?
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