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Figure 12–32 shows various positions of a child on a swing moving toward a person on the ground who is blowing a whistle. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

Short Answer

Expert verified

The highest frequency of sound will be heard at position C while the child is swinging forward.

Step by step solution

01

Understanding Simple Harmonic Motion

Simple Harmonic Motion is repetitive back and forth movement through an equilibrium so that the maximum displacement on one side of the equilibrium position is equal to the maximum displacement on the other side.

The force responsible for the motion is always directed toward the equilibrium position and is directly proportional to its distance.

02

Detailed Explanation

Let us assume that the child is moving with Simple Harmonic Motion (SHM), and in SHM, the highest speed is at the equilibrium point. Thus the highest speed of the child is at the equilibrium point, point C. And to have an increased pitch, the relative motion of the source and detector must be toward each other. The child would also hear the lowest frequency of sound at point C while swinging backward.

Hence, the highest sound frequency will be heard at position C when the child is swinging forward, while the lowest sound frequency will be heard at position C when the child is swinging backward.

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Most popular questions from this chapter

Question: Two loudspeakers are at opposite ends of a railroad car as it moves past a stationary observer at\({\bf{12}}{\bf{.0}}\,{\bf{m/s}}\), as shown in Fig. 12–41. If the speakers have identical sound frequencies of \({\bf{348}}\,{\bf{Hz}}\), what is the beat frequency heard by the observer when (a) he listens from position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

Fig. 12-41

A single mosquito 5.0 m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 200 such mosquitoes?

Question: A dramatic demonstration, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For an \({\bf{80}}\)-cm-long rod, (a) what is the fundamental frequency of the sound? (b) What is its wavelength in the rod, and (c) what is the traveling wavelength of the sound in air at\({\bf{2}}{{\bf{0}}^{\bf{o}}}{\bf{C}}\)?

Sound waves are

(a) transverse waves characterized by the displacement of

air molecules.

(b) longitudinal waves characterized by the displacement

of air molecules.

(c) longitudinal waves characterized by pressure

differences.

(d) Both (b) and (c).

(e) (a), (b), and (c).

How far from the mouthpiece of the flute in Example 12–11 should the hole be that must be uncovered to play \({\bf{F}}\) above middle \({\bf{C}}\) at \({\bf{349}}\;{\bf{Hz}}\)?

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