Question

A wave of amplitude 0.4 m interferes with a second wave of amplitude 0.23 m traveling in the same direction. What is the largest resultant amplitude that can occur? Answer in units of m

Answer 1

Resultant amplitude is 0.53 m.

Step-by-step explanation:

Amplitude is defined as the maximum displacement of wave particles from their respective mean positions.

The resulting amplitude of any two waves is given by the relation :

A =
`\sqrt{A_(1) ^(2) + A_(2) ^(2) + 2A_(1)A_(2)\cos x }`

Here, A is resultant amplitude, A₁ and A₂ are the amplitudes of two waves respectively and x is the difference in phase angle of the two waves.

According to the problem, A₁ is 0.4 m , A₂ is 0.23 m and x is zero. So, the above equation becomes,

A =
`\sqrt{0.4^(2) + 0.23^(2) + 2* 0.4* 0.23* cos 0 }`

A =
`√(0.16 + 0.053 + 0.184 )`

A = 0.63 m