For a standing wave mode on a string fixed at both ends, adjacent antinodes are separated by a distance of 20 cm. Waves travel on this string at a speed of 12 m/s. At what frequency is the string vibrated to produce this standing wave?

Question

BlackTom AI · Accepted Answer

Adjacent antinodes are separated by half a wavelength (λ/2), so λ/2 = 20 cm.

1) Relevant knowledge points and concepts
- For standing waves on a string fixed at both ends, consecutive antinodes (and consecutive nodes) are spaced by λ/2.
- Wave speed, wavelength, and frequency are related by v = fλ.

2) Step-by-step reasoning
- Start from the antinode spacing: λ/2 = 20 cm.
- Convert to meters: 20 cm = 0.20 m.
- Solve for the wavelength: λ = 2 × 0.20 m = 0.40 m.
- Use the wave relation with given speed v = 12 m/s to find frequency: f = v/λ.

3) Calculations (intermediate steps shown)
- λ = 2 × 0.20 m = 0.40 m
- f = v / λ = 12 m/s ÷ 0.40 m = 30 s^−1 = 30 Hz

4) Why the correct answer is correct
- The computed frequency 30 Hz satisfies both the geometric standing-wave constraint (antinode separation = λ/2) and the dispersion relation v = fλ for the given wave speed. Thus the physical conditions uniquely give f = 30 Hz.

5) Why the other options are incorrect (briefly)
- a. 20 Hz → λ = v/f = 12/20 = 0.60 m ⇒ λ/2 = 0.30 m (not 0.20 m).
- c. 40 Hz → λ = 12/40 = 0.30 m ⇒ λ/2 = 0.15 m (not 0.20 m).
- d. 60 Hz → λ = 12/60 = 0.20 m ⇒ λ/2 = 0.10 m (not 0.20 m).
- e. 120 Hz → λ = 12/120 = 0.10 m ⇒ λ/2 = 0.05 m (not 0.20 m).
None of these give the required 0.20 m spacing.

6) Conclusion
The correct frequency is 30 Hz, which matches answer b. 30 Hz.

For a standing wave mode on a string fixed at both ends, adjacent antinodes are separated by a distance of 20 cm. Waves travel on this string at a speed of 12 m/s. At what frequency is the string vibrated to produce this standing wave?单项选择题

类似问题

For a standing wave formed within an open ended air column, which of the following statements describe the condition at both ends?

If the length between two fixed points of a resonating string is L, and L= wavelength/2, then the standing waves is the

If the length between two fixed points of a resonating string is L, and L= wavelength, then the standing waves is the

If the length between two fixed points of a resonating string is L, and L= 3 x wavelength/2, then the standing waves is the

A closed organ pipe has

In a stationary wave, nodes are at Blank 1 Question 5[select: , fixed points, movable points, there are no nodes, random points]

A guitar string playing a note shows a stationary wave. At the centre is:

A standing wave is observed in a string. The distance between the nodes is 0.5 m. The wavelength is therefore:

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