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Chapter 19: Problem 28

A sound wave in a fluid medium is reflected at a barrier so that a standing wave is formed. The distance between nodes is \(3.84 \mathrm{~cm}\) and the speed of propagation is \(1520 \mathrm{~m} / \mathrm{s}\). Find the frequency.

Short Answer

Expert verified
The frequency of the standing wave in the fluid is approximately \(19805 Hz\).

Step by step solution

01

Convert the Distance between Nodes into Wavelength

The distance between nodes in the standing wave is given as \(3.84 cm\). However, this represents half a wavelength. So, the total wavelength \(\lambda\) is \(2 \times 3.84 cm = 7.68 cm\). Convert it to meters by dividing by 100, so \(\lambda = 0.0768~m\).
02

Calculate the Frequency

The speed of sound \(v\) in the medium is \(1520 m/s\), and it equals the product of the wavelength \(\lambda\) and the frequency \(f\), i.e., \(v = f \cdot \lambda\). Substituting the given values we can find the frequency \(f\) by re-arranging to \(f = v / \lambda\). This gives \(f = 1520~m/s / 0.0768~m = 19805~Hz\).

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Most popular questions from this chapter

A bat is flitting about in a cave, navigating very effectively by the use of ultrasonic bleeps (short emissions of highfrequency sound lasting a millisecond or less and repeated several times a second). Assume that the sound emission frequency of the bat is \(39.2 \mathrm{kHz}\). During one fast swoop directly toward a flat wall surface, the bat is moving at \(8.58 \mathrm{~m} / \mathrm{s}\). Calculate the frequency of the sound the bat hears reflected off the wall.

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