Allied & ICAR Exam Bank • ALLIED_2726 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Partial Differential Equations – Laplace, heat and wave equations

Question Statement:

A vibrating string of length $L = 1\text{ m}$ fixed at both ends has wave speed $c = 100\text{ m/s}$. The fundamental natural frequency in Hertz ($f_1 = c / (2L)$) is:

Answer Key:

50

Step-by-Step Solution & Explanation

$f_1 = \frac{c}{2L} = \frac{100}{2 \times 1} = 50\text{ Hz}$.
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