Question

The length of a sonometer wire is $0.75m$ and density $9\times {10}^{3}k/m^3$It can bear a stress of $8.1\times {10}^{8}N/m^2$ with out exceeding the elastic limit The fundamental frequency that can be produced in the wire,is

• A. $200Hz$
• B. $150Hz$
• C. $600Hz$
• D. $450Hz$

Answer 1

The correct option is A $200Hz$

Given, $Length=0.75m,density=9\times {10}^{3}k/m^3,Stress=8.1\times {10}^{8}N/m^2$

Let the area of the wire be A.

So, $Stress=8.1\times {10}^8\Rightarrow Density=\frac{mass}{volume},mass=Density\times volume$

$=9\times {10}^3(0.75\times A)=9\times {10}^{3}l\times A$ Where l is the length

$Mass=6.75\times {10}^3\times A\Rightarrow C=\sqrt{\frac{T}{mass/unit}}=\sqrt{\frac{8.1\times {10}^8\left(A\right)}{\frac{6.75\times {10}^3\times A}{0.75}}}=300m/s$

$f=\frac{c}{2l}=\frac{300}{1.5}=200Hz$