Question

The ends of a stretched wire of length $l$ are fixed at $x=0$ and $x=l$ . In one experiment, the displacement of the wire is $y_{1}=asin \left(\frac{\pi x}{l}\right)\left(sin ⁡ \omega t\right)$ and energy $E_{1}$ and in another experiment, its displacement is $y_{2}=asin \left(\frac{3 \pi x}{l}\right)\left(sin ⁡ 3 \omega t\right)$ and energy is $E_{2}$ then

• A. $E_{2}=E_{1}$
• B. $E_{2}=3E_{1}$
• C. $E_{2}=\frac{E_{1}}{3}$
• D. $E_{2}=9E_{1}$

Answer 1

Answer: (D)

In first case freq. $\Rightarrow \omega _{1}=\omega $
In second case freq. $\omega _{2}=3\omega $
$\because Energy \, \alpha \left(f r e q .\right)^{2}$
$\frac{E_{1}}{E_{2}}=\frac{\omega^{2}}{(3 \omega)^{2}}$
$\Rightarrow E_{2}=9E_{1}$