A transverse wave y= 0.05sin(20πx−50πt) in metre, is propagating along +ve X-axis on a string where x is in metre and t is in second. A light insect starts crawling on the string with the velocity of 5 cm/s at t=0 along the +ve X-axis from a point where x=5 cm. After 5 s the difference in the phase of its position is equal to

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A transverse wave $y = 0.0 5sin (20 π x - 50 π t)$ in metre, is propagating along $+ v e$ X-axis on a string where x is in metre and t is in second. A light insect starts crawling on the string with the velocity of 5 cm/s at $t = 0$ along the $+ v e$ X-axis from a point where x=5 cm. After 5 s the difference in the phase of its position is equal to

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$150 π$

$250 π$

$10 π$

$5 π$

answer is D.

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Detailed Solution

$Δ \emptyset = \frac{2 π}{λ} . Δ x = k (Δ x) = k (v t) H e r e v t = d i s \tan c e t r a v e l l e d b y i n s e c t i n g i v e n t i m e i n t e r v a l . (O r) Δ \emptyset = (20 π) (5 \times 10^{- 2} \times 5) = 5 π$