To apply Problem-Solving Strategy 12.1 Standing waves and normal modes. A cellis

Question

To apply Problem-Solving Strategy 12.1 Standing waves and normal modes. A cellist tunes the C string of her instrument to a fundamental frequency of 65.4Hz. The vibrating portion of the string is 0.600m long and has a mass of 14.4g. With what tension must she stretch that portion of the string? What percentage increase in tension is needed to increase the frequency from 65.4Hz to 73.4Hz , corresponding to a rise in pitch from C to D? What percentage increase in tension, Delta FT/FT, is needed to increase the frequency from 65.4 Hz to 73.4 Hz, corresponding to a rise in pitch from C to D? Enter your answer as a percentage to three significant figures. Think about whether your results make sense. If you change one of the given quantities, do the results change in a predictable way?

Explanation / Answer

V = T / (m/L)

(fundamental ) = 2 * L

= 2 * 0.600

= 1.2 m

---------------------------------

V = * f

= 1.2 * 65.4

= 78.48 m/s

T = V2 * ( m/L )

= 6159 * 0.0144 / 0.6

= 147.8 N
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% increase in frequency

= (8 / 65.4) . 100

= 12.2 %

The Tension must increase by a square root factor meaning a percentage increase of 6.1%

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