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Chapter 12: Q18P (page 328)

Question: (II) Two sound waves have equal displacement amplitudes, but one has 2.2 times the frequency of the other. What is the ratio of their intensities?

Short Answer

Expert verified

The ratio of intensities of sound waves is \(4.84\).

Step by step solution

01

Understanding the relation between the intensity and frequency of sound

In this problem, for estimating the ratio of intensities utilize the relation between frequency and intensity.

02

Given data

The frequency of one sound wave is \({f_1} = 2.2{f_2}\).

Here, \({f_2}\) is the frequency of other sound wave.

03

Evaluating the ratio of intensity of sound waves

The ratio of intensities of sound waves is calculated below:

\(\frac{{{I_1}}}{{{I_2}}} = {\left( {\frac{{{f_1}}}{{{f_2}}}} \right)^2}\)

Substitute the values in the above equation.

\(\begin{array}{c}\frac{{{I_1}}}{{{I_2}}} = {\left( {\frac{{2.2{f_2}}}{{{f_2}}}} \right)^2}\\\frac{{{I_1}}}{{{I_2}}} = 4.84\end{array}\)

Hence, the ratio of intensities of sound waves is \(4.84\).

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Most popular questions from this chapter

Question: (II) (a) Estimate the power output of sound from a person speaking in normal conversation. Use Table 12-2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. (b) How many people would it take to produce a total sound output of 60 W of ordinary conversation? (Hint: Add intensities, not dBs.)

A stone is dropped from the top of a cliff. The splash it makes when striking the water below is heard 2.7 s later. How high is the cliff?

A sailor strikes the side of his ship just below the water line. He hears the echo of the sound reflected from the ocean floor directly below 2.0 s later. How deep is the ocean at this point? Assume the speed of sound in sea water is 1560 m/s (Table 12-1) and does not vary significantly with depth.

Question: A bat emits a series of high-frequency sound pulses as it approaches a moth. The pulses are approximately \({\bf{70}}{\bf{.0}}\,{\bf{ms}}\) apart, and each is about \({\bf{3}}{\bf{.0}}\,{\bf{ms}}\) long. How far away can the moth be detected by the bat so that the echo from one pulse returns before the next pulse is emitted?

Question: (III) When a player鈥檚 finger presses a guitar string down onto a fret, the length of the vibrating portion of the string is shortened, thereby increasing the string鈥檚 fundamental frequency (see Fig. 12鈥�36). The string鈥檚 tension and mass per unit length remain unchanged. If the unfingered length of the string is l= 75.0 cm, determine the positions x of the first six frets, if each fret raises the pitch of the fundamental by one musical note compared to the neighboring fret. On the equally tempered chromatic scale, the ratio of frequencies of neighboring notes is 21/12.

Figure 12-36
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