Height of the receiving and transmitting antenna in communication of a signal are 245 m and 180 m respectively. Find the maximum distance between the two antennas for proper communication.
- 104 km
- 208 km
- 52 km
- 96 km
The Correct Option is A
Solution and Explanation
Understanding the Problem
We need to find the maximum distance in the line of sight between two antennas using the formula:
\( d = \sqrt{2Rh_t + 2Rh_r} \)
where:
- \( R = 6400 \, \text{km} \) (radius of the Earth)
- \( h_t = 180 \, \text{m} \) (height of the transmitting antenna)
- \( h_r = 245 \, \text{m} \) (height of the receiving antenna)
Corrected Solution
1. Convert Units:
Since \(R\) is in kilometers, we need to convert \(h_t\) and \(h_r\) to kilometers.
\( h_t = 180 \, \text{m} = 0.18 \, \text{km} \)
\( h_r = 245 \, \text{m} = 0.245 \, \text{km} \)
2. Substitute Values into the Formula:
\( d = \sqrt{2(6400)(0.18) + 2(6400)(0.245)} \)
\( d = \sqrt{2(6400)(0.18 + 0.245)} \)
\( d = \sqrt{12800(0.425)} \)
\( d = \sqrt{5440} \)
3. Calculate the Distance:
\( d \approx 73.76 \, \text{km} \)
Error in Your Calculation
You directly added the heights in meters and multiplied them by the radius in kilometers without converting the heights to kilometers. This led to a significantly larger and incorrect result.
Final Answer
The maximum distance in the line of sight between the two antennas is approximately \( 73.76 \, \text{km} \).
Top JEE Main Physics Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
Top JEE Main communication systems Questions
Find the correct combination of A, B, C and D inputs which can cause the LED to glow.
Identify the correct truth table of the given logic circuit.
- In AM modulation, a signal is modulated on a carrier wave such that maximum and minimum amplitude are found to be $6 V$ and $2 V$ respectively The modulation index is
- If the height of the tower used for LOS communication is increased by 21%, the percentage change in range is?
- Which of the following frequencies does not belong to FM broadcast?
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
Concepts Used:
Communication Systems
A system that describes the information exchange between two points is called the communication system. The transmission and reception process of information is called communication. The major elements of communication are such as:
- The Transmitter of information
- Channel or medium of communication
- The Receiver of information
Examples Of Communication Systems:
The following are the examples of communication systems:
- Internet
- Public Switched Telephone network
- Intranet and Extranet
- Television
Types Of Communication Systems:
Turning on Signal specification or technology, the communication system is categorized as follows:
- Analog technology communicates data as electronic signals of differing frequencies or amplitude. For instance Broadcast and telephone transmission.
- In Digital technology, the data are created and processed in two states: High (represented as 1) and Low (represented as 0). Also this technology stores and transmits data in the form of 1's and 0's.
Elements of a Communication System:
