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Chapter 12: Q12-Q (page 328)

In Fig. 12–16, if the frequency of the speakers is lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer together? Explain.

Short Answer

Expert verified

The point D and C will move farther apart.

Step by step solution

01

Meaning of interference and relationship between the wavelength and frequency

Interference is when two coherent waves superimpose to produce a greater, smaller, or same amplitude wave.

The frequency of a wave is inversely proportional to the wave's wavelength. Thus, wavelength increases on decreasing the frequency.

02

Step 2: Find what happens to points D and C when the frequency is lowered

The distance between the points of constructive and destructive interference depends on the wave's wavelength. If the wavelength increases, then the distance between the points also increases. So, if the speakers' frequency is lowered, then the wavelength of the wave will increase, and so the distance between the points D and C.

Hence, the points D and C would move farther apart.

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Most popular questions from this chapter

(II) The two sources of sound in Fig. 12–16 face each other and emit sounds of equal amplitude and equal frequency (305 Hz) but 180° out of phase. For what minimum separation of the two speakers will there be some point at which (a) complete constructive interference occurs and (b) complete destructive interference occurs. (Assume T = 20°C.)

Question: (III) When a player’s finger presses a guitar string down onto a fret, the length of the vibrating portion of the string is shortened, thereby increasing the string’s fundamental frequency (see Fig. 12–36). The string’s 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

To make a given sound seem twice as loud, how should a musician change the intensity of the sound?

(a) Double the intensity.

(b) Halve the intensity.

(c) Quadruple the intensity.

(d) Quarter the intensity.

(e) Increase the intensity by a factor of 10.

At a rock concert, a dB meter registered 130 dB when placed 2.5 m in front of a loudspeaker on stage. (a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air? (b) How far away would the sound level be 85 dB?

What is the sound level of a sound whose intensity is\(1.5 \times {10^{ - 6}}\;{\rm{W/}}{{\rm{m}}^2}\)?
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