1. Tardigrade
  2. Question
  3. Physics
  4. 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 1 mm 2 and density 8000 kg / m 3. What is the tension in the string?

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Q. 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 $1\, mm ^{2}$ and density $8000\, kg / m ^{3}$. What is the tension in the string?

Waves

Solution:

$y=0.02 \sin (x+30 t)$
For the given wave: $v=\frac{d x}{d t}=-30$
($x+30 t=$ constant)
We have
$v=\sqrt{\frac{T}{\mu}} \Rightarrow T=\mu v^{2}=A \cdot \rho V^{2}$
$=\left(10^{-6} m ^{2}\right)\left(8 \times 10^{3} \frac{ kg }{ m ^{3}}\right)(30)^{2}$
$\Rightarrow T= 7.2\, N$