A-level Physics (Advancing Physics)/Bandwidth/Worked Solutions

1. A broadband internet connection has a bit rate of 8Mbit s⁻¹ when downloading information. What is the minimum bandwidth required to carry this bit rate?

$2B=8\times 10^6$

$B=\frac{8\times 10^6}{2}=4\times 10^6\text{ Hz}=4\text{ MHz}$

2. The same connection has a bandwidth of 100 kHz reserved for uploading information. What is the maximum bit rate that can be attained when uploading information using this connection?

b = 2 x 100 x 10³ = 200 x 10³ bits / second = 24.4 kbytes / second

3. A lighthouse uses a flashing light and Morse Code to communicate with a nearby shore. A 'dash' consists of the light being on for 2s. The light is left off for 1s between dots and dashes. What is the bandwidth of the connection?

One bit takes 3 seconds to transmit.

$B=\frac{1}{3}\text{ Hz}\approx 333\text{ mHz}$

4. The broadband connection in question two is used to upload a 1Mbyte image to a website. How long does it take to do this?

The bit rate is 200 x 10³ bits / second.

1 Mbyte = 1048576 bytes = 8388608 bits.

$b=\frac{\text{no. of bits}}{\text{no. of seconds}}$

$200\times 10^3=\frac{8388608}{\text{no. of seconds}}$

$\text{no. of seconds}=\frac{8388608}{200\times 10^3}\approx 42\text{ s}$