Given that,
Mass density of the string, μ=4×10−3 kg/m
Tension, T=360 N
Frequency of first resonance, f1=375 Hz
Next higher frequency, f2=450 Hz
We can write,
f1=375=n2l√Tμ and f2=450=n+12l√Tμ
where n is number of segments vibrating.
f2f1=450375=n+1n⇒n=5
So, length of string l=n2×f1√Tμ=52×375√3604×10−3=2 m
⇒ Mass of wire =(μ)(l)=(4×10−3×2)=8×10−3 kg