Question

Three waves of equal frequency having amplitudes \(13\ \mu \text{m}\), \(6\ \mu \text{m}\), \(5\ \mu \text{m}\) arrive at a given point with successive phase difference of \(\pi /2\). The amplitude of the resultant wave is (in \(\mu \text{m}\)) \((\cos 90^{\circ }=0,\,\cos \pi =-1)\)

• A. \(15\)
• B. \(10\)
• C. \(8\)
• D. \(4\)

Hint:

Add the amplitudes as phasors at 0, 90 and 180 degrees.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Successive phase difference \(\dfrac{\pi}{2}\) means phasors of amplitudes 13, 6 and 5 point at \(0\), \(\dfrac{\pi}{2}\) and \(\pi\).

Step 2: Components
Along the first direction: \(13-5=8\).
Along the perpendicular direction: \(6\).

Step 3: Resultant
\(A=\sqrt{8^{2}+6^{2}}=\sqrt{100}=10\ \mu\text{m}\)

Final Answer:
The resultant amplitude is 10 micrometres. \[ \boxed{\text{(B) }10} \]