Question

A string of length 40 cm and weighing 10 g is attached to a spring at one end and to a fixed wall at the other end. The spring has a spring constant of 160 N 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

Time Needed is 0.05 s

Explanation:

Given,

Length of the string, L = 40 cm

Mass of the string = 10 gm

Mass per unit length =$\frac {10}{40}$ = 14 ($gmcm^-^1$) = 1040 = 14 $gmcm^-^1$

Spring constant, k = $160\ Nm^-^1$

Deflection, x=1 cm = 0.01 m

Tension, T= kx = $160 \times 0.01$

⇒ T = 1.6 N = $16\times 10^4$ dyn

Now, v = $\sqrt(\frac {T}{m})$  

= $\sqrt(\frac {16\times 10^4}{1/4})$

v = $8\times 10^2\ cms^-^1$

= $800\ cms^-^1$

∴ Time taken by the pulse to reach the spring,  

t = $\frac {40}{800}$

= $\frac {1}{20}$  

= 0.05 s