A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, y(x, t) = (0.01 m) sin [(62.8 m–1) x] cos [(628 s–1)t]. Assuming p = 3.14, the correct statement(s) is (are)

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A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, y(x, t) = (0.01 m) sin [(62.8 m^–1) x] cos [(628 s^–1)t]. Assuming p = 3.14, the correct statement(s) is (are)

The length of the string is 0.25 m

The fundamental frequency is 100 Hz

The number of nodes is 5

The maximum displacement of the midpoint of the string, from its equilibrium position is 0.01 m

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(A) 6

(B) $\frac{5 λ}{2} = L$

$K = \frac{2 π}{λ} \Rightarrow λ = \frac{2 π}{K} = 0 .1 m$

$∴ L = \frac{5 λ}{2}$

= 5 × 0.1 $\frac{1}{2}$ = 0.25 m

$∴$ 0.01 m

(D) w = 628 = 2 $π$ f₅

f₅ = 40 Hz

$∴$ fundamental = 8 Hz

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