A wire having a linear density 0 1kg/m is kept under a tension of 490 N It is observed - Physics - Waves

Question

A wire having a linear density 0 1kg/m is kept under a tension of
490 N It is observed that it resonates at a frequency of 400Hz The
next higher frequency is 450 Hz Find the length of the wire

Sanjay Singh · Accepted Answer

Dear student
Formula of velocity on the string isv=Tμ=4900
1=4900=70m/sLet length of the wire be l
Let the wire vibrate forming n loops when it resonates with 400Hz
so l=nλ12
1v=f×λ170=400×λ1λ1=70400 l=nλ12=n2×70400=n2×740
2Let the wire vibrate forming (n+1 )loops when it resonates with 450Hz
 l=(n+1)λ22
1v=f×λ270=450×λ2λ1=70450 l=(n+1)λ22=n2×70450=(n+1)2×745
3from eqn 2 and 3n2×740=(n+1)2×745n8=n+199n=8n+8n=8from eqn 3l=(8+1)2×745=92×745=710=0
7m=70cmRegards

A wire having a linear density 0.1kg/m is kept under a tension of 490 N. It is observed that it resonates at a frequency of 400Hz. The next higher frequency is 450 Hz. Find the length of the wire