Question

The linear density of a vibrating string is $1.3\times 10^{- 4} \, kg \, m^{- 1}$ . A transverse wave is propagating on the string and its described by the equation $y=0.021sin \left(x + 30 t\right)$ , where $x$ and $y$ are measured in $m$ and $t$ in $s$ . The tension in the string is

• A. $0.12 \, N$
• B. $0.48 \, N$
• C. $1.20 \, N$
• D. $4.80 \, N$

Answer 1

Answer: (A)

$m=1.3\times 10^{- 4} \, kg \, m^{- 1}$
From Eq., $k=1 \, m^{- 1} \, $ , $\omega =30 \, s^{- 1}$
Wave velocity $v=\frac{\omega }{k}=30m / s$
Wave speed on vibrating string,
$v=\sqrt{\frac{T}{m}}$
$30=\sqrt{\frac{T}{1.3 \times 1 0^{- 4}}}$
$T=\left(1.3 \times 1 0^{- 4}\right)900$
$T=0.12 \, N$