The speed of a wave on a string is 150 `"ms"^(-1)` when the
tension is 120 N. The percentage increase in the
tension in orderr to raise the wave speed by `20%` is

Options

A. 0.44
B. 0.4
C. 0.2
D. 0.1

Answer

A

Explanation

Wave speed
`v=sqrt((T)/(mu))`
`impliesvpropsqrt(T)implies(v_(1))/(v_(2))=sqrt((T_(1))/(T_(2)))implies(T_(1))/(T_(2))=((v_(1))/(v_(2)))^(2)`
`[v_(1)=150m//s,v_(2)=v_(1)+20%,"of "v_(1)=150+30=180m//s]`
`implies (T_(2)-T_(1))/(T_(1))=(v_(2)^(2)-v_(1)^(2))/(v_(1)^(2))`
`implies((T_(2)-T_(1))/(T_(1)))%=((180)^(2)-(150)^(2))/((150)^(2))=0.44=44%`