Question

You are continuing to investigate the sounds that you can make from your roommate's guitar, as described in the opening storyline. You decide to take some data. One particular string is of length 64.2 cm and plays a note with a fundamental frequency of 196 Hz when it is allowed to vibrate freely along its entire length. You now press the string down strongly against a fret that is located 21.4 cm from the end of the string by the tuning pins. You pluck the string and use a smartphone app to measure the fundamental frequency ffret of the sound. Next, you touch your finger lightly at the same position as before, a technique that will result in the string playing what guitarists call a "harmonic." You pluck the string and use the smartphone app to measure the frequency ftouch of the sound. What are the frequencies ffret and ftouch (in Hz)? ffret = ! ftouch = Hz

Answer 1

When La 64.2 cm fundamental frequency f = 196 hz. harelegth of sound ware d = 2l = 128.4 cm. relority = 41 = 196 X 128.4 then steing is pressed at a distance 214 cm from th tuning pin , dength of string allowed to vibrate is 64.2 – 21.4. 42.8 cm. weredagth of found here in this come, to 42.8 x 2 frequerey fleet = 4 - 196 X 128.4 = 294 hz. - 42.8*2

If he touch at the same position lightly, we haceasure 3rd harmonics of full stug lugth because 21.4 is % of 64.2. to ftouch - 3*196 = 588 hz.