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(B) The equation of the wave is $y = y_0 \sin 2\pi \left( ft - \frac{x}{\lambda} \right)$.The particle velocity $v_p$ is given by the derivative of di

Vedclass · Accepted Answer

$\lambda = \frac{\pi y_0}{2}$

Vedclass · Answer

(B) The equation of the wave is $y = y_0 \sin 2\pi \left( ft - \frac{x}{\lambda} \right)$.The particle velocity $v_p$ is given by the derivative of displacement with respect to time: $v_p = \frac{\partial y}{\partial t} = y_0 (2\pi f) \cos 2\pi \left( ft - \frac{x}{\lambda} \right)$.The maximum particle velocity is $V_{\max} = 2\pi f y_0$.The wave velocity $V$ is given by $V = f\lambda$.According to the problem,$V_{\max} = 4V$.Substituting the expressions,we get: $2\pi f y_0 = 4(f\lambda)$.Dividing both sides by $f$,we get: $2\pi y_0 = 4\lambda$.Therefore,$\lambda = \frac{2\pi y_0}{4} = \frac{\pi y_0}{2}$.

List-$I$	List-$II$
$(1)$ Planck's constant	$(i)$ $[ML^{-1} T^{-2}]$
$(2)$ Gravitational constant	(ii) $[ML^{-1} T^{-1}]$
$(3)$ Bulk modulus	(iii) $[ML^2 T^{-1}]$
$(4)$ Coefficient of viscosity	(iv) $[M^{-1} L^3 T^{-2}]$

Column-$I$	Column-$II$
$(a)$ $Oscillatoria$	$(p)$ $Prothallus$
$(b)$ $Cycas$	$(q)$ $Cell$ $wall$ $contains$ $chitin$ $mixed$ $with$ $cellulose$
$(c)$ $Dryopteris$	$(r)$ $Primitive$ $flowers$
$(d)$ $Yeast$	$(s)$ $Food$ $stored$ $as$ $starch$

$A$ transverse wave is described by the equation $y = y_0 \sin 2\pi \left( ft - \frac{x}{\lambda} \right)$. The maximum particle velocity is equal to four times the wave velocity if

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