Question #109817

A cello string vibrates in its fundamental

mode with a frequency of 242 1/s. The vibrating segment is 91 cm long and has a mass

of 0.82 g.

Find the tension in the string.

Answer in units of N

Find the frequency of the string when it

vibrates in three segments.

Answer in units of 1/s.

mode with a frequency of 242 1/s. The vibrating segment is 91 cm long and has a mass

of 0.82 g.

Find the tension in the string.

Answer in units of N

Find the frequency of the string when it

vibrates in three segments.

Answer in units of 1/s.

Expert's answer

Let's calculate "\\mu" ="\\frac{0.82\\times10^{-3}}{0.91}=0.9\\times10^{-3}"

"v=\\frac1{2l}\\sqrt{\\frac{T}{\\mu}}=\\frac{1}{2\\times0.91}\\sqrt{\\frac{T}{0.9\\times10^{-3}}}"

"242\\times2\\times0.91\\times30=\\sqrt T\\\\\\sqrt T=13213.2\\\\T=174588654.24 N"

when string is divided into 3 segments then the frequency becomes 3 times of fundamental frequency

then the frequency is 3"\\times242" =726 Hz

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