Answer:
The length of the string is [tex]\frac17[/tex] m.
Explanation:
Data provided in the question:
Velocity, V = 200 m/s
Initial frequency [tex]\Rightarrow f_1=550 \ Hz,[/tex]
Final frequency, [tex]\quad f _{2}=700\ Hz[/tex]
Now, we know
[tex]\Rightarrow \lambda=\frac Vf\\ \Rightarrow \lambda_{1}=\frac{v}{f_1}\\ =\frac{200}{560}=\frac{2}{5 .6}=\frac {2.5}7[/tex]
and,
[tex]\qquad \lambda_{2}=\frac V {f_2}=\frac{200}{700}=\frac{2}{7}[/tex][tex]\text { Here } \lambda_{1}=2 \lambda+\frac \lambda {2}=\frac{5 \lambda}{2}=2.5 \lambda[/tex]
also,
[tex]\lambda=l=\frac{2.5}7\times\frac 1 {2.5}=\frac{1}{7}[/tex]
Therefore,
The length of the string is [tex]\frac17[/tex] m.
