Question

The equation of a stationary wave along a stretched string is given by y = 5 sin x cos 40pt where x and y are in cm and t is in s. The separation between two adjacent nodes is

• A. 1.5 cm
• B. 3 cm
• C. 6 cm
• D. 4 cm

Answer 1

Answer: (A)

1.5 cm

Answer 2

The given equations of a stationary wave is

$y = 5\sin\frac{2\pi}{3}x\cos 40\pi t$ ….(i)

The standard equations of a stationary wave is

$y = 2a\sin kx\cos\omega t$ ….(ii)

Comparing (i) and (ii), we get

$k = \frac{2\pi}{3}$

Or $\frac{2\pi}{3} = \frac{2\pi}{3}or\lambda = 3cm$

Separations between two adjacent nodes is

$\frac{\lambda}{2} = \frac{3}{2} = 1.5cm$