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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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Most popular questions from this chapter

You have a stopped pipe of adjustable length close to a taut 62.0-cm, 7.25-g wire under a tension of 4110 N. You want to adjust the length of the pipe so that, when it produces sound at its fundamental frequency, this sound causes the wire to vibrate in its second overtone with very large amplitude. How long should the pipe be?

A 75.0-cm-long wire of mass 5.625 g is tied at both ends and adjusted to a tension of 35.0 N. When it is vibrating in its second overtone, find (a) the frequency and wavelength at which it is vibrating and (b) the frequency and wavelength of the sound waves it is producing.

A long tube contains air at a pressure of 1.00 atm and a temperature of 77.0°C. The tube is open at one end and closed at the other by a movable piston. A tuning fork that vibrates with a frequency of 500 Hz is placed near the open end. Resonance is produced when the piston is at distances 18.0 cm, 55.5 cm, and 93.0 cm from the open end. (a) From these values, what is the speed of sound in air at 77.0°C? (b) From the result of part (a), what is the value of g? (c) These results show that a displacement antinode is slightly outside the open end of the tube. How far outside is it?

A person is playing a small flute 10.75cm long, open at one end and closed at the other, near a taut string having a fundamental frequency of 600.0Hz. If the speed of sound is 344.0m/s , for which harmonics of the flute will the string resonate? In each case, which harmonic of the string is in resonance?

A piano wire with mass 3.00 g and length 80.0 cm is stretched with a tension of 25.0 N. A wave with frequency 120.0 Hz and amplitude 1.6 mm travels along the wire. (a) Calculate the average power carried by the wave. (b) What happens to the average power if the wave amplitude is halved?

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