# 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?

${\displaystyle 2B=8\times 10^{6}}$

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

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.

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

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.

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

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

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