The top string of a guitar has a fundamental frequency of 310 Hz when it is allowed to vibrate as a whole, along all its 65.0 cm length from the neck to the bridge. A fret is provided for limiting vibration to just the lower two-thirds of the string.
(a) If the string is pressed down at this fret and plucked, what is the new fundamental frequency?
(b) The guitarist can play a "natural harmonic" by gently touching the string at this fret and plucking the string at about one sixth of its length from the bridge. What frequency will be heard then?