Question

A string of length 40 cm and weighing 10 g is attached to a spring at one end to a fixed wall at the other end. The spring has a spring constant of $160N{m}^{-1}$ and is stretched by 1.0 cm. If a wave pulse is produced on the string near the wall, how much time will it take to reach the spring ?

Answer 1

L = 40 cm, mass = 10 gm... mass per unit length

$=\frac{10}{40}=\frac{1}{4}\left(gm/cm\right)$

Spring constant, k = 160 N/m

Deflection = x = 1 cm

= 0.01 m

$\Rightarrow T=kx=160\times 0.01$

$=1.6N=16\times {10}^4$ dyne

Again, $v=\sqrt{\left(\frac{T}{m}\right)}=\sqrt{\left(\frac{16\times {10}^4}{\frac{1}{4}}\right)}$

$=8\times {10}^{2}cm/s=800cm/s$

$\therefore$ Time taken by the pulse to reach the spring

$t=\frac{40}{800}=\frac{1}{20}=0.05sec$