Stationary wave is produced along the stretched string of length 80 cm. The resonant frequencies of string are 90 Hz, 150 Hz and 210 Hz. The speed of transverse wave in the string is (a) 45 m/s (b) 75 m/s (c) 48 m/s (d) 80 m/s

Answer: (c). The given frequencies 90, 150, 210 Hz are all multiples of 30 Hz (their HCF), so take the fundamental f₀ = 30 Hz. For a string fixed at both ends, f₀ = v/2L, so v = 2Lf₀. v = 2 × 0.80 × 30 = 48 m/s. So the answer is (c) 48 m/s.

Stationary wave is produced along the stretched string of length 80… | MHT CET 2024 (10 May, Shift 2)

Q40MHT CET 2024 · 10 MAY · SHIFT 2Easy

Stationary Waves & Vibrating Strings

Stationary wave is produced along the stretched string of length 80 cm. The resonant frequencies of string are $90\text{ Hz}, 150\text{ Hz}$ and 210 Hz. The speed of transverse wave in the string is

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Answer: (c)

The given frequencies $90, 150, 210\text{ Hz}$ are all multiples of $30\text{ Hz}$ (their HCF), so take the fundamental $f_0 = 30\text{ Hz}$ .
For a string fixed at both ends, $f_0 = \dfrac{v}{2L}$ , so $v = 2Lf_0$ .
$v = 2 \times 0.80 \times 30 = 48\text{ m/s}$ .
So the answer is (c) $48\text{ m/s}$ .

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