A cellist tunes the C string of her instrument to a fundamental frequency of 65.

Question

A cellist tunes the C string of her instrument to a fundamental frequency of 65.4 Hz . The vibrating portion of the string is 0.600 m long and has a mass of 14.4 g . With what tension must she stretch that portion of the string? What percentage increase in tension is needed to increase the frequency from 65.4 Hz to 73.4 Hz , corresponding to a rise in pitch from C to D?

Part C

To determine the wave speed from purely kinematic quantities, you need to know the wavelength of the wave. What is the wavelength of the fundamental mode in the C string of the cello?

Express your answer in meters.

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Explanation / Answer

Formua for frequency f = nv/2L

where 2Lterm Corresponds to Wavelength

V is Velocty , V^2 = T/u

where T is tension and u is linear mass density = m/l

so T = V^2 * m/L

since v = 2Lf

T = 4 L^2 f^2 m/l   

T = 4* 0.6* 0.6 * 65.4 * 65.4 * 0.0144/0.6

T = 147.8 N

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since T is proportiona to f^2

T2/T1 = f2^2/f1^2

T2 = 147.8 *(73.4/65.4)^2

T2 = 186.18 N

% change in Tension = (T2-T1)/T1 * 100

= 186.18 - 147.8 /147.8

= 25.96 % or 26 %

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wavength L = 2l = 2 * 0.6 = 1.2 m

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