Physics

Problem

Two sound waves of the same frequency travel in the same direction through still air. The first wave has displacement amplitude

A_1

while the second has displacement amplitude

A_2

. The phase of the second wave leads that of the first by a constant angle

\phi

. a. (i) Write an expression for the resultant displacement at any instant when the two waves overlap. b. (ii) Derive an expression for the resultant amplitude

A

in terms of

A_1

A_2

and

\phi

. c. (iii) Using your result, obtain expressions for (a) the maximum possible intensity and (b) the minimum possible intensity in terms of

A_1

and

A_2

. d. (iv) If

A_1=3\,\text{mm}

and

A_2=4\,\text{mm}

, calculate the ratio of the maximum intensity to the minimum intensity.

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