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 $π = 3.14$ , the correct statement(s) is (are) [2013]

Question

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 $π = 3.14$ , the correct statement(s) is (are) [2013]

Smart Achievers · Accepted Answer

(2, 3)

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

$From the given equation, k = \frac{2 π}{λ} = 62.8$

$∴$ $λ = \frac{2 π}{62.8} = 0.1 m$

Length of string, $l = 5 \times \frac{λ}{2} = 5 \times \frac{1}{20} = 0.25 m$

The midpoint $M$ is an antinode and has the maximum displacement $= 0.01 m$

The fundamental frequency, $ν = \frac{v}{2 l} = \frac{ω / k}{2 l}$

$= \frac{628}{2 \times 0.25 \times 62.8} = 20 Hz$

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