Question

The average power transmitted through a given point on a string with a sine wave is 0.40 watt, when the amplitude of the wave is 2mm. What average power will be transmitted through this point its amplitude is increased to 4 mm

• A. 0.40 watt
• B. 0.80 watt
• C. 1.2 watt
• D. 1.6 watt

Answer 1

The correct option is D 1.6 watt

Average power of a wave is

$P_{avg}=\frac{1}{2}\mu w^2{A}^{2}V\Rightarrow P_{avg}\alpha A^2\left(always\right)$

$\therefore \frac{P_1}{A_1^2}=\frac{P_2}{A_2^2}\frac{P_1}{P_2}={\left(\frac{P_1}{P_2}\right)}^2$

Given $A_1=2mm$

$A_2=4mm$

$\frac{P_1}{P_2}={\left(\frac{2}{4}\right)}^2{P}_1=\frac{1}{4}\times P_2{P}_2=4P_1=4\times 0.4\therefore [P_2=1.6watt]$

Hence option (D) is correct