Question

Sinusoidal waves 5.00 cm in amplitude is to be transmitted along a string having a linear mass density equal to $4.00\times {10}^{-2}kg/m$. If the source can deliver an average power of 90 W and the string is under a tension of 100 N then the highest frequency at which the source can operate is (take ${\pi }^2=10$)

• A. 45 Hz
• B. 50 Hz
• C. 30 Hz
• D. 62 Hz

Answer 1

The correct option is C 30 Hz

A=$5cm=0.05m$

$\mu =4\times {10}^{-2}kg/m{P}_{avg}=90WT=100N$

Since,

$P_{avg}=\frac{1}{2}\mu w^2{A}^{2}V{P}_{avg}=\frac{1}{2}\mu \times {\left(2\pi f\right)}^2{A}^2\sqrt{\frac{T}{\mu }}{P}_{avg}=\frac{1}{2}\times 4\times {10}^{-2}\times 4{\pi }^2\times f^2\times {\left(0.05\right)}^2\times \sqrt{\frac{100}{4\times {10}^{-2}}}{P}_{avg}=80\times 0.0025\times {10}^{-2}\times f^2\times \frac{100}{2}90=10\times {10}^{-2}\times f^2\Rightarrow [f=30Hz]$

Hence option (C) is correct.