Question

The equations of two waves are given by :
y₁ 5 sin2π (x - vt) cm

y₂ 3 sin2π (x - vt + 1.5) cm

These waves are simultaneously passing through a string. The amplitude of the resulting wave is ______.

Options

• 2 cm

• 4 cm

• 5.8 cm

• 8 cm

Answer 1

The equations of two waves are given by :
y₁ 5 sin2π (x - vt) cm

y₂ 3 sin2π (x - vt + 1.5) cm

These waves are simultaneously passing through a string. The amplitude of the resulting wave is 2 cm.

Explanation:

A = `sqrt("A"_1^2+"A"_2^2+2"A"_1"A"_2cosphi)`

where Φ = phase difference

= [(x - vt + 1.5) - (x - vt)] × 2π

= 2π × 1.5

= 3π

So, A = `sqrt(5^2+3^2+2.5.3cospi)`

= `sqrt4`

= 2 cm.