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A 5.00 m, 0.732 kg wire is used to support two uniform 235 N posts of equal length (Fig. P15.55), Assume that the wire is essentially horizontal and that the speed of sound is 344 m/s. A strong wind is blowing, causing the wire to vibrate in its 5th overtone. What are the frequency and wavelength of the sound this wire produces?

Short Answer

Expert verified

Thus, the frequency is \(2064\;Hz\) and wavelength is \(0.166\;m\).

Step by step solution

01

Given in the question

Speed of sound \(v = 344\;{\rm{m/s}}\).

The mass of wire \(m = 0.732\;{\rm{kg}}\).

Length of wire \(L = 5.00\;m\)

Tension on the wire \(F = 235\;{\rm{N}}\).

02

Use formula of frequency and wavelength

The speed is\(v = \lambda f = \sqrt {\frac{F}{\mu }} \).

Thus, the formula for frequency and wavelength is given by:

\(f = \left( {pth\;overtone + 1} \right) \times velocity\;of\;sound\;in\;air\)

Here, \(F\) is tension, \(\mu \) is linear density, \(\lambda \) is wavelength and \(f\) is frequency.

03

Calculate the frequency and wavelength

According to the question,

The frequency is calculated as follows:

\(\begin{array}{c}f = \left( {5 + 1} \right) \times 344\\ = 6 \times 344\\ = 2064\;Hz\end{array}\)

Thus, the wavelength is calculated as follows:

\(\begin{array}{c}v = \lambda f\\344 = \lambda \times 2064\;Hz\\\lambda = \frac{{344}}{{2064}}\\ = \frac{1}{6}\\ = 0.166\;m\end{array}\)

Hence, the frequency is \(2064\;Hz\) and wavelength is \(0.166\;m\).

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