First slide

Standing waves

Question

The ends of a stretched wire of length L are fixed at x = 0 and x = L. ln one experiment, the displacement of the wire is $y_{1} = A \sin (\frac{πx}{L})$ and energy is $E_{1}$ , and in another experiment its displacement is $y_{2} = A \sin (\frac{2 πx}{L}) \sin 2 ωt$ and energy is $E_{2}$ . Then

Moderate

A

$E_{2} = E_{1}$
B

$E_{2} = 2 E_{1}$
C

$E_{2} = 4 E_{1}$
D

$E_{2} = 16 E_{1}$

Solution

Energy (E) $\propto$ ${(Amplitude)}^{2} {(Frequency)}^{2}$ Amplitude is same in both the cases, but frequency 2 $ω$ in the second case is two times the frequency ( $ω$ ) in the first case. Hence $E_{2} = 4 E_{1}$

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