/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 18 A laptop computer communicates w... [FREE SOLUTION] | 91Ó°ÊÓ

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A laptop computer communicates with a router wirelessly, by means of radio signals. The router is connected by cable directly to the Internet. The laptop is \(8.1 \mathrm{m}\) from the router, and is downloading text and images from the Internet at an average rate of 260 Mbps, or 260 megabits per second. (A bit, or binary digit, is the smallest unit of digital information.) On average, how many bits are downloaded to the laptop in the time it takes the wireless signal to travel from the router to the laptop?

Short Answer

Expert verified
Approximately 702 bits are downloaded.

Step by step solution

01

Determine the Speed of Radio Signals

Radio signals travel at the speed of light, which is approximately \( 3 \times 10^8 \) meters per second. This is the speed we will use to calculate the time it takes for the signal to travel from the router to the laptop.
02

Calculate Time for Signal to Travel

We can calculate the time it takes for the radio signal to travel the \(8.1 \, \text{m}\) distance using the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}}. \] Thus, \( \text{Time} = \frac{8.1}{3 \times 10^8} \, \text{seconds} \).
03

Calculate the Number of Bits Downloaded

With the time calculated in Step 2 and the download rate of 260 Mbps, use \[ \text{Bits downloaded} = \text{Rate} \times \text{Time}, \] where the rate is \(260 \times 10^6\) bits per second. Therefore, \[ \text{Bits downloaded} = 260 \times 10^6 \times \frac{8.1}{3 \times 10^8}. \]
04

Simplify the Calculation

Simplify the expression to find the total number of bits downloaded in that short time interval: \[ \text{Bits downloaded} = \frac{260 \times 8.1}{3} \approx 702 \text{ bits}. \]
05

Final Calculation

Completing the multiplication and division, we find the approximate number of bits is 702. So, about 702 bits are downloaded to the laptop in the time it takes the signal to travel from the router to the laptop.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Radio Signals
Wireless communication, like the connection between a laptop and a router, uses radio signals to transmit data. These radio waves are a type of electromagnetic wave, similar to visible light but with a lower frequency. Electromagnetic waves can travel through different mediums, such as air, without the need for physical cables. This makes radio signals perfect for wireless communication.

Radio signals enable devices to communicate by sending and receiving data as electromagnetic waves. The antenna of a device, such as a router or a laptop, converts these waves into electrical signals that represent digital information. Without the need for physical connections, radio signals provide flexibility and mobility in our modern communication systems.
Speed of Light
In the realm of wireless communication, it's crucial to understand the speed of light. The speed of light in a vacuum is approximately \(3 \times 10^8\) meters per second. Radio signals, like any other electromagnetic wave, travel at this speed.

When calculating how long it takes for a signal to get from the router to your laptop, you use the formula:
  • \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\)
If your laptop is 8.1 meters away from the router, the travel time for the radio signals is calculated by substituting the distance and the speed of light into the equation. Understanding this speed helps us appreciate how quickly data travels over wireless connections.
Data Transfer Rate
Data transfer rate is a measure of how much digital information can be sent or received over a network in a given amount of time. It's usually measured in bits per second (bps). For the laptop in our scenario, the data transfer rate is given as 260 megabits per second (Mbps).

This means that, every second, 260 million bits of digital information could potentially be downloaded or uploaded through the wireless connection. Knowing the data transfer rate allows us to calculate how many bits are downloaded to the laptop in the time it takes for the signal to travel from the router. Using the known time for the signal to travel, you multiply it by the data transfer rate to find out how many bits were received in that interval.
Digital Information
In the context of data transfer, digital information is crucial as it defines the smallest unit of data, known as a bit. A bit can only have a value of 0 or 1, which corresponds to the binary system used in computing.

When talking about downloading data, this digital information is packed into larger units called bytes, kilobytes, megabytes, etc. However, in terms of measuring the transfer rates over a network, we often refer to bits per second. This quantifies how much digital information, in terms of these smallest units, can move between devices like your laptop and a router. Understanding digital information helps in deciphering how effectively and efficiently data is being transferred in a wireless communication setup.

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Most popular questions from this chapter

A laser emits a narrow beam of light. The radius of the beam is \(1.0 \times 10^{-3} \mathrm{m},\) and the power is \(1.2 \times 10^{-3} \mathrm{W} .\) What is the intensity of the laser beam?

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