This is the reason broadband internet (ADSL) is called broadband. Because dial up internet used the POTS frequency band below 4 khz, and broadband used the (broad) frequencies above.
It's also the reason you'd have to get a technician out to your house in order to get ADSL. They would install a frequency cutoff filter on the phone line into your house, and hookup the landline to the below 4 khz side and the ADSL modem to the above 4 khz side, so the POTS signal would not interfere with the ADSL signal.