The equation of a wave travelling on a string is y = sin[20πx+ 10πt], where x and t are distance and time

Question

The equation of a wave travelling on a string is \(y = \sin[20\pi x + 10\pi t],\) where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

(1) 5.0 cm

(2) 20 cm

(3) 10 cm

(4) 2.5 cm

Answer 1

Correct option is : (1) 5.0 cm

Minimum distance between 2 points having same speed is \(\frac{\lambda}{2}.\)

\(\lambda = \frac{2\pi}{k} = \frac{1}{10}m = 10cm\)

Distance \( = \frac{\lambda}{2} = 5cm\)