Two speakers are placed side by side and driven by the same frequency of 500 Hz. If the distance from a person to one speaker is 5.00 m and the person detects little or no sound, which of the following is a possible the distance from the person to the other speaker? (The sound speed is 340 m/s.)

Question

BlackTom AI · Accepted Answer

For destructive interference the path difference must equal (n + 1/2)·λ, so start by finding the wavelength.

1) Relevant knowledge points and concepts
- Sound speed v, frequency f → wavelength λ = v / f.
- Destructive interference occurs when path difference Δ = |d2 − d1| = (n + 1/2)λ, where n is an integer (0,1,2,...).
- Constructive interference would require Δ = nλ (integer multiples of λ), which would be loud, not quiet.

2) Complete reasoning process step by step
- Given v = 340 m/s and f = 500 Hz, compute λ.
  λ = v / f = 340 m/s ÷ 500 Hz = 0.68 m.
- Known distance to one speaker: d1 = 5.00 m. We seek d2 from the list such that Δ = |d2 − 5.00| equals (n + 1/2)·0.68 m for some integer n.

3) Calculations (intermediate steps shown)
- For n = 0: Δ = 0.5·0.68 = 0.34 → d2 = 5.00 ± 0.34 = 4.66 or 5.34 (not listed).
- n = 1: Δ = 1.5·0.68 = 1.02 → d2 = 6.02 or 3.98 (not listed).
- n = 2: Δ = 2.5·0.68 = 1.70 → d2 = 6.70 or 3.30 (not listed).
- n = 3: Δ = 3.5·0.68 = 2.38 → d2 = 7.38 or 2.62 (7.38 close to 7.7 but not matching the half‑integer condition exactly).
- n = 4: Δ = 4.5·0.68 = 3.06 → d2 = 5.00 + 3.06 = 8.06 m ≈ 8.1 m (rounding to two significant figures gives 8.1 m).

4) Why the correct answer is correct
- d2 ≈ 8.06 m yields a path difference of 3.06 m = 4.5·λ, which is precisely a half‑integer multiple of the wavelength and thus produces destructive interference (little or no sound). The provided choice 8.1 m matches this value within rounding.

5) Why the other options are incorrect
- 7.7 m: Δ = 2.70 m; 2.70/0.68 ≈ 3.97 (not a half‑integer), so not destructive.
- 8.4 m: Δ = 3.40 m; 3.40/0.68 = 5.00 (an integer) → constructive interference (would be loud).
- 9.1 m: Δ = 4.10 m; 4.10/0.68 ≈ 6.03 (not a half‑integer), so not destructive.

6) Conclusion
The only listed distance consistent with destructive interference is 8.1 m, which matches the provided correct answer.

类似问题

A person stands between two speakers driven by the same source. Each speaker produces a tone with a frequency of 200 Hz on a day when the speed of sound is 330 m/s. The person is 1.65 m from one speaker and 4.95 m from the other. What type of interference does the person sense?

A nodal line is

Two adjacent sources each emit a frequency of 800 Hz in air where the velocity of sound is 340 m/s. How much farther back would source 1 have to be moved so an observer in front of the sources would hear no sound?

Match the following statements 1: Condition for constructive interference pattern 2: Destructive interference produces 3: Two sources are coherent 4: Condition for destructive interference pattern 5: Constructive interference produces

Wave interference can occur for

Two small openings in a ripple tank are 3.0 cm apart. The tank is 1.2 m long, and the wavelength is 0.60 cm. At what distance from the central maximum will the third bright fringe appear?

Many product packages and ID cards use hologram stickers that change colour with viewing angle. Which wave phenomenon makes this possible, and how does it impact society?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单