Pitch perfect 2
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- 1. Pitch Perfect 2 By: Teresa Chang
- 2. What is a capo? A capo is a clamp used on neck of stringed instruments, such as guitars, banjos and mandolins Purpose: Shorten playable length of strings to increase the pitch (aka the frequency)
- 3. Why use a capo? The fingerings (orientation of fingers on each string) remains unchanged when a capo is used compared to when it is open (without a capo). In other words, capos make playing higher notes easier!
- 4. Standing waves on guitars Since the strings on a guitar are fixed on both ends (via tuning pegs and bridge base of guitar), when a string is plucked, standing waves are created as the wave oscillates back and forth, and reflected from fixed ends
- 5. Problem Part A: If I pluck an open string (without a capo) of linear mass density 7.28g/m on a guitar, the tension of the guitar string Im playing is 96.882 N and I measure the length of string as 70cm, what is the frequency of the string without a capo on? Assume all frequencies produced on the guitar are fundamental frequencies. Part B: If I want to use a capo to play a higher note that is double the frequency of the open string, at what length from the bridge of the guitar should I place my capo in order to produce this new pitch?
- 6. Part A- Step 1: Write down known values
- 7. Part A- Step 2: Plug into equation Use the fundamental frequency equation:
- 8. Part B- Step 1: Write down known values Tension and linear mass density are properties that remain unchanged from part A because you are using the same string.
- 9. Part B- Step 2: Manipulate equation and plug values in 1) Use fundamental frequency equation. 2) Multiply both sides by 2L2. 3) Divide both sides by f2. 4) Divide both sides by 2. 5) Plug values in. Result: The new frequency is proportional to the length of the string of the old frequency.
- 10. Making sense of your answer The frequency calculated from part A corresponds to the string E2 (you can Google this). From part B, to play a pitch of 164.8Hz, the capo must be 35cm away from the bridge which corresponds to the 12th fret of the guitar. Your new note is now E3. You can actually measure this! Length of E2 string measured from tuning peg to bridge base of guitar Length of E2 string measured is 70cm
- 11. Making sense of your answer Unfortunately, on classical guitars, the 12th fret is where the sound board is, so you cant actually put a capo there. But it works on acoustic guitars! Length of string from 12th fret to bridge base of guitar Length of E3 string measured is 35cm