First slide

Travelling wave

Question

A transverse wave described by equation $y = 0.02 \sin (x + 30 t)$ (where x and t are in metre and sec. respectively) is travelling along a wire of area of cross-section $1 {mm}^{2}$ and density $8 g / cc$ . What is the tension in the string? (in Newtons)

Moderate

Solution

Given
Area of cross section $A = 1 {mm}^{2}$
$A = 10^{- 6} m^{2}$
We use
$y = 0.02 \sin (x + 30 t)$ for the given wave:
Wave Speed, $v = \frac{ω}{k} = 30$ m/s
We have wave speed $v = \sqrt{\frac{T}{μ}}$
$\Rightarrow T = μ v^{2} = A ρ V^{2}$ $= (10^{- 6} m^{2}) (8 \times 10^{3} kg / m^{3}) {(30)}^{2}$
$\Rightarrow T = 7.2 N$

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