First slide

Travelling wave

Question

A travelling wave on a string is given by $y = 7.5 \sin (0.005 x + 12 t + π / 4)$ . Find the displacement and velocity of the particle at a point $x = 1 c m$ $t = 1 \sec$ . Take $[\sin ({12.7}^{o}) = 0.22]$ .

Moderate

A

1.65 cm, 87.8 cm/sec
B

4 cm, 70.2 cm/sec
C

1.72 cm, 870 cm/sec
D

1 cm, 10 cm/sec

Solution

$G i v e n y = 7.5 \sin (0.005 x + 12 t + π / 4) \to (i) P u t t i n g x = 1 c m a n d t = 1 \sec i n e q (i) w e h a v e y = 7.5 \sin (0.005 \times 1 + 12 \times 1 + \frac{3.142}{4}) = 7.5 \sin (12.79 r a d) = 7.5 \sin ({732.7}^{0}) (π r a d = 180^{0}) = 7.5 \sin (4 π + {12.7}^{0}) = 7.5 \sin ({12.7}^{0}) = 7.5 \times 0.22 = 1.65 c m P a r t i c l e v e l o c i t y i s o b t a i n e d b y d i f f e r e n t i a t i n g (i) w . r . t t i m e t v = d y / d t = 7.5 \times 12 \times c o s (0.005 x + 12 t + π / 4) P u t t i n g x = 1 c m a n d t = 1 \sec \begin{array}{l} v = 7.5 \times 12 \times c o s ({12.7}^{0}) \\ = 87.8 c m / \sec \end{array}$

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