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JEE Main 2019 (9 Apr, Shift 2) · Stationary Waves & Vibrating Strings

Stationary Waves & Vibrating Strings question from JEE Main 2019 (9 Apr, Shift 2)

Q91JEE Main 2019 · 9 APR · SHIFT 2Easy

Stationary Waves & Vibrating Strings

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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Answer: (d)

Third harmonic: $L = \dfrac{3\lambda}{2} \Rightarrow \lambda = \dfrac{2 \times 2.0}{3} = \dfrac{4}{3}\text{ m}$ .
$v = f\lambda = 240 \times \dfrac{4}{3} = 320\text{ m/s}$ .
Fundamental $f_0 = \dfrac{240}{3} = 80\text{ Hz}$ .
So the answer is (d) $320\text{ m/s}, 80\text{ Hz}$ .

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