Question

If two waves represented by $y₁=4 \sin ω t$ and $y₂=3 \sin(ω t+\frac\pi3)$ interfere at a point. The amplitude of the resulting wave will be about

• A. 7
• B. 6
• C. 5
• D. 3.5

Hint:

If two waves represented by $y1=4 \sin ω t$ and $y2=3 \sin(ω t+π/3)$ interfere at a point. The amplitude of the resulting wave will be about

Answer 1

The Correct Option is B

Step 1: Formula
Resulting amplitude $A = \sqrt{a_{1}^{2}+a_{2}^{2}+2a_{1}a_{2} \cos \phi}$.
Step 2: Values
$a_{1} = 4, a_{2} = 3, \phi = \pi/3 = 60^{\circ}$.
Step 3: Calculation
$A = \sqrt{4^{2} + 3^{2} + 2(4)(3) \cos 60^{\circ}}$ $A = \sqrt{16 + 9 + 24(0.5)} = \sqrt{25 + 12} = \sqrt{37} \approx 6.08$.
Hence, the Answer is: (B)