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Physics - Wave on String Question with Solution | TestHub

PhysicsWave on String321Hard2 minQB

PhysicsHardmultiple choice

Two waves given by equation $y_{1} = A sin (ω t - kx)$ and $y_{2} = 4 A sin (2 ω t - 4 kx)$ are traveling in two different strings having same mass per unit length and same cross-sectional area. Tension in first string is four times tension in the second string.

Options:(select one or more)

Answer:

A, B

Solution:

$v = \frac{T}{μ}$ ; $T_{1} = 4 T_{2}$ gives $v_{1} = 2 v_{2}$ , so (D) is wrong

$U \propto μ ω^{2} A^{2}$ : $\frac{U _{1}}{U _{2}} = \frac{ω ^{2} A ^{2}}{4 ω ^{2} \cdot 16 A ^{2}} = \frac{1}{64}$ (A)

$I \propto μ ω^{2} A^{2} v$ : $\frac{I _{1}}{I _{2}} = \frac{1}{64} \times 2 = \frac{1}{32}$ (B); power ratio is also 1/32, not 1/16

Answers (A, B)

Stream:JEESubject:PhysicsTopic:Wave on StringSubtopic:321

⏱ 2mℹ️ Source: QB

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