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

The fundamental frequency is

100 H z

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The number of nodes is 5

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The length of the string is

0.25 m

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

0.1 m

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Solution

The correct option is D The maximum displacement of the midpoint of the string, from its equilibrium position is $0.1 m$
No. of nodes = 6, $λ = \frac{2 π}{K} = \frac{2 \times 3.14}{62.8} = 0.1 m$

Length = $\frac{5 λ}{2} = 0.25 m$
The mid-point is antinode. Its maximum displacement = $0.01 m$
$f = \frac{v}{2 l} = \frac{ω}{K \times 2 l} = 20 H z$

Suggest Corrections

Similar questions

y (x, t) = (0.01 m) sin [(62.8 m^{- 1}) x] cos [(628 s^{- 1}) t]

π = 3.14

y (x, t) = 0.01 m sin [(62.8 m^{- 1}) x] cos [(628 s^{- 1}) t] .

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