Question 152: Waves

Question

The equations of two waves are given by :
y1 = 5 sin 2$$\pi$$(x - vt) cm
y2 = 3 sin 2$$\pi$$(x $$-$$ vt + 1.5) cm
These waves are simultaneously passing through a string. The amplitude of the resulting wave is :

Accepted Answer

$${y_1} = 5\sin (2\pi x - 2\pi vt)$$
$${y_2} = 3\sin (2\pi x - 2\pi vt + 3\pi )$$
$$\Rightarrow$$ Phase difference = 3$$\pi$$
$$ \Rightarrow {A_{net}} = \sqrt {A_1^2 + A_2^2 + 2{A_1}{A_2}\cos (3\pi )} $$
$$ \Rightarrow {A_{net}} = 2$$ cm

Answer

2 cm

Answer

4 cm

Answer

5.8 cm

Answer

8 cm

Waves

The equations of two waves are given by : y1 = 5 sin 2$\pi(x - vt) cm y2 = 3 sin 2\pi(x -$ vt + 1.5) cm These waves are simultaneously passing through a string. The amplitude of the resulting wave is :

Choose the correct answer: