Solution: Is the acceleration of a simple harmonic

Chapter 5, Problem 53P

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QUESTION:

(I) A violin string vibrates at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)

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QUESTION:

(I) A violin string vibrates at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)

ANSWER:

Solution 53P

When a string is plucked a standing wave is formed. The ends are the nodes and the center is the antinode so if the length of string is L the wavelength is 2L. When fingered at ⅓rd length the  length that vibrates is ⅔ L. The wavelength reduces and we will have a higher frequency.

Step 1 of 2 ^

Frequency of the vibration (/)= 294 Hz

Length of the string = L

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