A-level Physics (Advancing Physics)/Bandwidth

Bandwidth is the frequency of a signal. Although original signals have varying frequencies, when these are transmitted, for example, as FM radio waves, they are modulated so that they only use frequencies within a certain range. FM radio modulates the frequency of a wave, so it needs some variation in the frequencies to allow for transmission of multiple frequencies. Since bandwidth is a frequency, it is the number of bits per. second. The bandwidth required to transmit a signal accurately can be calculated by using 1 as the number of bits, giving the formula:

$B={\frac {1}{t}}$

where B is bandwidth (in Hz), and t is the time taken to transmit 1 bit of data (in s).

The bandwidth of a signal regulates the bit rate of the signal, as, with a higher frequency, more information can be transmitted. This give us the formula (similar to the formula for lossless digital sampling):

b = 2B

where b is the bit rate (in bits per. second), and B is the bandwidth (in Hz).

Questions

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?

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?

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?

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?

Worked Solutions