A sonometer wire under a tension of N10N, produces a frequency of 250Hz when plucked....

WAEC 1998

A sonometer wire under a tension of N10N, produces a frequency of 250Hz when plucked. Keeping the length of the wire constant, the tension is adjusted to produce a new frequency of 350Hz. Calculate the new tension

A. 39.2N
B. 19.6N
C. 14.2N
D. 7.4N
E. 5.1N

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Correct Answer: Option B

Explanation

f \(\alpha\) \(\sqrt{T}\)

\(\frac{f_1}{f_2} = \sqrt{\frac{T_1}{T_2}}\)

\(\frac{250}{350} = \sqrt{\frac{10}{T_2}}\)

\(\frac{5}{7} = \sqrt{\frac{10}{T_2}}\)

\(\frac{25}{49} = \frac{10}{T_2}\)

T² = \(\frac{49 \times 10}{25} = 19.6\)

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