Displacement - time graphs for two waves, wave - 1 and wave - 2 are shown here. The ratio of the intensity of wave - 1 to that of wave - 2 is

Question

Displacement - time graphs for two waves, wave - 1 and wave - 2 are shown here. The ratio of the intensity of wave - 1 to that of wave - 2 is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-r0otjbjwztgk.png" /> (A) 1:1 (B) 9:4 (C) 16:9 (D) 9:1

Tardigrade Admin · Accepted Answer

Average intensity along the string < I> =2π 2f2A2Ï±v (l1/l2)=((f1 A1/f2 A2))2=((T2 A1/T1 A2))2=((1/2) × 3)2=(9/4)

Q. Displacement - time graphs for two waves, wave - $1$ and wave - $2$ are shown here. The ratio of the intensity of wave - $1$ to that of wave - $2$ is

$1 : 1$

$9 : 4$

$16 : 9$

$9 : 1$

Average intensity along the string
$< I > = 2 π^{2} f^{2} A^{2} ϱ v$
$\frac{l _{1}}{l _{2}} = (\frac{f _{1} A _{1}}{f _{2} A _{2}})^{2} = (\frac{T _{2} A _{1}}{T _{1} A _{2}})^{2} = (\frac{1}{2} \times 3)^{2} = \frac{9}{4}$

Q. Displacement - time graphs for two waves, wave - 1 and wave - 2 are shown here. The ratio of the intensity of wave - 1 to that of wave - 2 is

1:1

9:4

16:9

9:1