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Vibrations of a string fixed at both ends are represented by $y = 10 \sin (\frac{π}{20} x) Cos (90 πt)$ , where x,y are in ‘cm’ and ‘ t ’ in seconds. The phase difference between the points x=15 cm And x = 25cm in radians is

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$\frac{π}{5}$

$π$

$\frac{π}{2}$

answer is B.

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Detailed Solution

$\begin{array}{l} y = 2 ASin kxCos ω t = 10 Sin \frac{π}{20} x \\ Cos (90 πA) \\ K = \frac{2 π}{λ} = \frac{π}{20} ∴ \frac{λ}{2} = 20 cm \\ x = 15 cm is in 1^{st} loop, x = 25 cm is in \\ 2^{nd} loop. Hence Δϕ = π \end{array}$

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