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

Answer:

Resultant amplitude is 0.53 m.

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 = $\sqrt{0.4^{2} + 0.23^{2} + 2\times 0.4\times 0.23\times cos 0 }$

A = $\sqrt{0.16 + 0.053 + 0.184 }$

A = 0.63 m