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  • A transverse wave traveling in a string Produces maximum transverse velocity of <img alt="5 \mathrm{~m} / \mathrm{s}" src="https://entrancecorner.oncodecogs.com/gif.latex?5%20%5Cmathrm%7B%7Em%7D%20

A transverse wave traveling in a string Produces maximum transverse velocity of 5 \mathrm{~m} / \mathrm{s} and maximum transverse acceleration 110 \mathrm{~m} / \mathrm{s}^{2} in a Particle. If the velocity of the wave in the string is 30 \mathrm{~m} / \mathrm{s}. Determine the equation of the wave.

Option: 1

y=0.22 \sin \left(12 t \pm \frac{15}{11} x+\varphi\right)


Option: 2

y=0.22 \sin \left(10 t \pm \frac{11}{15} x+\varphi\right)


Option: 3

y=0.22 \sin \left(22 t \pm \frac{11}{14} x+\varphi\right)


Option: 4

y=0.22 \sin \left(22 t \pm \frac{11}{15} x+\varphi\right)


Answers (1)

best_answer

A \omega=5                    ----- (1)

A \omega^2=110                   -------- (2)

(1) divide by (2)

$$ \begin{aligned} \frac{A \omega}{A \omega 2} & =\frac{5}{110} \\ \frac{1}{\omega} & =\frac{1}{22} \\ \omega & =22 \mathrm{~s}^{-1} \end{aligned}

$$ \begin{aligned} & A w=5 \\ & A \times 22=5 \\ & A=\frac{5}{22}=0.22 m \\ & K=\frac{w}{V} \\ & K=\frac{22}{30}=\frac{11}{15} \\ & y=A \sin (\omega t \pm k n+\varphi) \\ & y=0.22 \sin \left(22 t \pm \frac{11}{15} x+\varphi\right) \end{aligned}

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Ajit Kumar Dubey

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