Question

A guitar string is clamped at the nut and the bridge. When you pluck the string, you set up a standing wave on it. The “scale” of the guitar is the distance from nut to bridge, typically 64 cm.(a) [4 pts.] The low A string on a guitar is supposed to produce a note with a frequency of 110 Hz. What is the speed of sound on this string?(b) [3 pts.] If the pitch is too high, you can lower the frequency of the note by slacking the tension on the string. Explain how this lowers the frequency.(c) [3 pts.] To produce a higher-frequency note, you can fret the string – clamping it with your finger somewhere between the nut and the bridge. Explain how this raises the frequency.(d) [4 pts.] A decent guitarist can get the string to play “harmonics” – overtones of the fundamental frequency (110 Hz for the A string). What are the frequencies of the next two overtones of the A string?(e) [5 pts.] Suppose I invented a bridge that allows the string to move freely up and down, rather than clamping it in place. Would this make the guitar a higher- or lower-pitched instrument? What frequency would I get from the A string?(f) [6 pts.] What would be the frequencies of the next two overtones of the A string on my guitar with the new bridge?

Answer 1