Question

Sinusoidal waves 5.00 cm in amplitude are to be transmitted along a string that has a linear mass density equal to 4.00 × 10^-2 kg/m. If the source can deliver a maximum power of 300 W and the string is under a tension of 100 N, then the highest frequency at which the source can operate is:

• A. 45.3 Hz
• B. 50.4 Hz
• C. 55.1 Hz
• D. 62.3 Hz

Answer 1

Answer: (C)

55.1 Hz

Answer 2

P = $\frac{1}{2}$m ω²A²V using V = $\sqrt{\frac{T}{\mu}}$

P = $\frac{1}{2}\omega$²A² $\sqrt{T\mu}$

ω = $\sqrt{\frac{2P}{A^{2}\sqrt{T\mu}}}$

f = $\frac{\omega}{2\pi} = \frac{1}{2\pi}\sqrt{\frac{2P}{A^{2}\sqrt{T\mu}}}$

using data f = 55.1 Hz.