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  4. A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is :

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Q. A string $2.0\, m$ long and fixed at its ends is driven by a $240\, Hz$ vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is :

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Solution:

$3\left(\frac{v}{2\ell}\right) =240 $
$ 3 \frac{v}{2\times2} = 240 $
$v = 320\, m/s$
fundamental frequency $ = \frac{v}{2\ell} = \frac{320}{2\times2} = 80 $