The equation of a transverse wave travelling along a string is Y(x, t) = 4.0 sin [20 x 10^{-3} x + 600t]

Question

The equation of a transverse wave travelling along a string is \(\mathrm{y}(\mathrm{x}, \mathrm{t})=4.0 \sin \left[20 \times 10^{-3} \ \mathrm{x}+600 \mathrm{t}\right] \mathrm{mm}\), where x is in the mm and t is in second. The velocity of the wave is :

(1) \(+30 \mathrm{~m} / \mathrm{s}\)

(2) \(-60 \mathrm{~m} / \mathrm{s}\)

(3) \(-30 \mathrm{~m} / \mathrm{s}\)

(4) \(+60 \mathrm{~m} / \mathrm{s}\)

Answer 1

Correct option is : (3) – 30 m/s

\(k = 20 \times 10^{-3}\ mm^{-1} = 20\ m^{-1}\) 

\(w = 600\ s^{-1}\)

\(v = \frac{w}{k} = \frac{600}{20} = 30\ m/s\) 

and x & t carry same sign

Therefore \(v = -30\ m/s\)