Shape of string transmitting wave along x - axis at some instant is as shown Velocity of point P is v = 4π cm/s and angle θ = tan

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Question

Shape of string transmitting wave along x - axis at some instant is as shown Velocity of point P is v = 4π cm/s and angle θ = tan^–1 (0.004π)

Velocity of wave is 10 m/s

Amplitude of wave is 2 mm

Max acceleration of particle is 80 π² cm/sec²

Wave is traveling in –ve x-direction

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$tanθ = \frac{\partial y}{\partial x} = \frac{4 π}{1000} = \frac{v_{p}}{v}$

$\frac{4 π}{100 v}$

⟹ v = 10 m/s
λ = 100 cm = 1m
⟹ f = 10 Hz
v_max = Aω

$\frac{4 π}{100} = A \times 2 π \times 10$

⟹ A = 2mm

${Aω}^{2} = \frac{4 π}{100} \times 20 π = \frac{4 π^{2}}{5} m / s^{2}$