Question

The equation of a wave disturbance is given as y = 0.02 sin$\left( \frac{\pi}{2} + 50\pi t \right)$cos (10 px), where x and y are in metres and t is in seconds. Choose the correct statement(s) –

• A. The wavelength of wave is 0.2 m
• B. Displacement node occurs at x = 0.15 m
• C. Displacement antinode occurs at x = 0.3 m
• D. All of the above

Answer 1

Answer: (D)

All of the above

Answer 2

From the given expression for y :

amplitude A = 0.02 m

angular frequency w = 50 p rad/s

and wave number k = 10 p m^–1

Now wave speed v =$\frac{\omega}{k}$=$\frac{50\pi}{10\pi}$= 5 m/s

Therefore, option (4) is wrong.

Displacement node occurs at

10 px =$\frac{\pi}{2}$, $\frac{3\pi}{2}$etc.

or x =$\frac{1}{20}$,$\frac{3}{20}$

or x = 0.05 m and 0.15 m

Displacement antinode occurs at

10 px = 0, p, 2p, 3p etc.

or x = 0, 0.1 m, 0.2 m and 0.3 m

Wavelength l = 2 (distance between two consecutive nodes or antinodes)

= 2(0.1) = 0.2 m