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?'''

$$2B = 8 \times 10^6$$

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

'''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.

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

'''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.

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

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

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