A 1.0-g string that is 0.64 m long is fixed at both ends and is under tension.This string produces a 100-Hz tone when it vibrates in the third harmonic.The speed of sound in air is 344 m/s.The tension in the string,in is closest to
A) 2.8 N.
B) 2.3 N.
C) 1.8 N.
D) 3.4 N.
E) 3.9 N.

Question

Quizplus · Accepted Answer

The speed of a wave on a string is given by $v = \sqrt{\frac{T}{\mu}}$, where $T$ is the tension in the string and $\mu$ is the linear mass density of the string. For the third harmonic on a string fixed at both ends, the frequency $f$ is given by $f = \frac{3v}{2L}$, where $L$ is the length of the string. Rearranging the formula for $v$ to solve for $T$ and substituting the given values, we find $T$ is closest to 2.8 N.

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