A stationary wave set up on a string have the equation $y = (2\text{ mm}) \sin [(6.25\text{ m}^{-1}) x \cos…
A stationary wave set up on a string have the equation $y = (2\text{ mm}) \sin [(6.25\text{ m}^{-1}) x \cos (\omega t)]$. This stationary wave is created by two identical waves each of amplitude $A$ moving in opposite directions along the string. Then,
(a) $A = 2\text{ mm}$
(b) $A = 4\text{ mm}$
(c) the smallest length of the string is 50 cm
(d) the smallest length of the string is 2 m
Solution
Amplitude, $A = \frac{2}{2} = 1\text{ mm}$
From the given equation, we can see that $k = 6.25\text{ m}^{-1}$.
The smallest length of string is equivalent to a single loop or length of string equal to $\frac{\lambda}{2}$ or $\frac{\pi}{k}$.
$\cdot\!\cdot\!\cdot\, L_{\min} = \frac{\pi}{k} = \frac{\pi}{6.25} = 0.5\text{ m} = 50\text{ cm}$