Q81 / 90 · JEE Main 2019 (09 Apr Shift 2) · Physics

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

Solution

For a string fixed at both the ends,

f = \frac{n}{2 L} v

For third harmonic,

240 = \frac{3}{2 (2)} v

\Rightarrow v = \frac{240 \times 4}{3}

= 320 m s^{- 1}

Fundamental frequency

f_{0} = \frac{1}{2 L} v

= \frac{1}{4} \times 320 = 80 H z

Hence, the correct answer is option: 'B'.