1. Tardigrade
  2. Question
  3. Physics
  4. Sinusoidal waves 5.00 cm in amplitude are to be transmitted along a string having a linear mass density equal to 4.00 × 10-2 kg / m. If the source can deliver a maximum 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 π2=10 ):

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Q. Sinusoidal waves $5.00\, cm$ in amplitude are 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 a maximum 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 $\pi^{2}=10$ ):

Waves

Solution:

We use power transmitted is given as
$P=\frac{1}{2} \mu \omega^{2} A^{2} V$ using $V=\sqrt{\frac{T}{\mu}}$
$\Rightarrow P=\frac{1}{2} \omega^{2} A^{2} \sqrt{T \mu}$
$\Rightarrow \omega=\sqrt{\frac{2 P}{A^{2} \sqrt{T \mu}}}$
$\Rightarrow f=\frac{\omega}{2 \pi}=\frac{1}{2 \pi} \sqrt{\frac{2 P}{A^{2} \sqrt{T \mu}}}$
$=30\, Hz$