Question

A $200$Hz wave with amplitude $1$mm travels on a long string of linear mass density $6$ g/m kept under a tension of $60$N. The total energy associated with the wave in a $2.0$m long portion of the string is?

• A. $9.4J$
• B. $9.4mJ$
• C. $18.8J$
• D. $18.8mJ$

Answer 1

The correct option is A $9.4J$

$A=1mm=10–3m,m=6g/m=6x10–3kg/m$

$T=60N,f=200hz$

$V=\sqrt{\frac{T}{M}}=100\frac{m}{s}$

$P_{avg}=2{\pi }^{2}mv{A}^2{f}^2=0.47w$

$t=\frac{2}{100}=0.02sec$

$Energy=2{\pi }^{2}mv{A}^2{f}^{2}t=9.46j$