Question

A string of length 20 cm and linear mass density 0⋅40 g cm−1 is fixed at both ends and is kept under a tension of 16 N. A wave pulse is produced at t = 0 near an ends as shown in figure (15-E3), which travels towards the other end. (a) When will the string have the shape shown in the figure again? (b) Sketch the shape of the string at a time half of that found in part (a).
Figure

Answer 1

Pulse Comes Back in 0.02 s

Explanation:

Given,  

Length of String = 20 cm

The linear mass density of the string = $0.40\ g cm^-^1$

Applied Tension = 16 N = $16 \times 10^5$ dyn

velocity of the wave:

v = $\sqrt \frac {T}{m}$

= $\sqrt \frac {16 \times 10^5}{0.4}$

= $2000 cm/s$

Time taken to reach other end  = $\frac {20}{2000}$ = 0.01 s

Time Taken to see the pulse again in the original position,  

= $0.01 \times 2$ = 0.02 s

(b) At 0.01 s, there will be a trough at the right end as it is reflected.