First slide

Equation of wave

Question

A transverse wave described by equation $y = 0.02 \sin (x + 30 t)$ (where x and t are in metres and seconds, respectively) is travelling along a wire of area of cross-section I ${mm}^{2}$ and density 8000 $kg / m^{3}$ . What is the tension in the string?

Moderate

A

20 N
B

7.2 N
C

30 N
D

14.4 N

Solution

$y = 0.02 \sin (x + 30 t)$
For the given wave:
(x+30t = constant)
$v = \frac{dx}{dt} = - 30$
$We have v = \sqrt{\frac{T}{μ}} \Rightarrow T = {μv}^{2} = A . {ρV}^{2}$
= $(10^{- 6} m^{2}) (8 \times 10^{3} \frac{kg}{m^{3}}) {(30)}^{2}$
$\Rightarrow T = 7.2 N$

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