`(a)` A string of mass 'm' and length 'L' is suspended from the ceiling and a mass M is hanged from it. Transverse waves are produced at its lowest point (nearM) having wavelength `lambda`, find its wavelength at a distance x from the upper point.
`(b)` In the previous question, what time a transverse pulse will take to reach from it lowest point to its uppermost point , if the mass M is not hanged from it

Explanation

`(a)` as `v` remains constant
`:.v=v.`
`:.(lambda)/(lambda.)=(lambda_(1))/(lambda_(2))=(v_(1))/(v_(2))=(sqrt(1))/(sqrt(2))=sqrt((Mg)/(Mg+(m(L-x))/(L)g)`
`(b) v=sqrt((T)/(m))=sqrt(((Mgx)/(L))/((M)/(L))) :.v=sqrt(gx)`
Now, `(dx)/(dt)=(gx)^(1//2)`
`:.int_(0)^(l)x^(-(1)/(2))dx=int_(0)^(t)sqrt(g)dt` `:.2sqrt(x)|_(0)^(L)=sqrt(g t)`
`:.2sqrt(L)=sqrt(g t)` `t=2sqrt((L)/(g))`