JEE PYQ: Waves And Sound Question 7
Question 7 - 2021 (26 Feb Shift 1)
The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form $y = -0.21\sin(x + 30t)$ is produced in it, where $x$ is in meter and $t$ is in second. Then, the expected value of tension in the wire is $x \times 10^{-2}$ N. Value of $x$ is __________. (Round-off to the nearest integer)
Show Answer
Answer: 1215
Solution
$y = -0.21\sin(x + 30t)$
$v = \frac{\omega}{K} = \frac{30}{1} = 30$ m/s
$v = \sqrt{\frac{T}{\mu}}$
$T = v^2 \times \mu$
$T = (30)^2 \times 0.135 \times 10^{-1}$ $\mu = 0.135$ g/cm
$T = 900 \times 0.135 \times 10^{-1}$ $\mu = 0.135 \times \frac{10^{-3}\text{ kg}}{10^{-2}\text{ m}}$
$T = 12.15$ N
$T = 1215 \times 10^{-2}$ N
$X = 1215$
BETA
