Question

A string of linear mass density 0⋅5 g cm−1 and a total length 30 cm is tied to a fixed wall at one end and to a frictionless ring at the other end (figure 15-E4). The ring can move on a vertical rod. A wave pulse is produced on the string which moves towards the ring at a speed of 20 cm s−1. The pulse is symmetric about its maximum which is located at a distance of 20 cm from the end joined to the ring. (a) Assuming that the wave is reflected from the ends without loss of energy, find the time taken by the string to region its shape. (b) The shape of the string changes periodically with time. Find this time period. (c) What is the tension in the string?
Figure

Answer 1

Frequency is Reciprocal of Time

Explanation:

The crest reflects as a crest here, Here, wire travels from denser to rarer medium, thereby making crest to reflect as crest.    

⇒ Phase change = 0  

a) To again original shape distance traveled by the wave S = 20+20 =40 cm.  

Wave speed, v = $20 ms^-^1$

=> $time = \frac {s}{v}$

= $\frac {40}{20} = 2 sec$

b) The wave regains its shape, after traveling a periodic distance = $2\times 30 = 60 cm$

Time period =$\frac {60}{20} =3 sec$.  

c) Frequency, n = $(\frac {1}{3})sec^-^1$

n =$(\frac {1}{2}l) \sqrt \frac {T}{m} (m 2x\times 30 =60cm$   = mass per unit length) =  $0.5 gcm^-^1$

T = $400 \times 0.5$

= 200 dyne

= $2 \times 10^-^3$ Newton