17.12
声波：共振
共振的产生取决于施加在波上的边界条件。 在对称边界条件（即两端都有一个节点）的张力下，弦可以产生共振。 节点被定义为字符串不移动的固定点。 对称边界条件导致某些频率共振并产生驻波，而其他频率则产生破坏性干扰。 声波可以在中空管中产生共振，共振的声波频率取决于边界条件。
例如，考虑一根一端封闭、另一端…
共振是系统中受迫振荡的一种特殊情况，当第一个物体的驱动力频率与第二个物体的固有频率相匹配时，会迫使第二个物体以相同频率振动，且振幅显著增大。
考虑一个音叉和一个一端封闭的空心圆柱管。当音叉的叉股以其固有频率振动时，会产生声波，该声波入射到管口，迫使管内的空气以相同频率振动。如果音叉的固有频率与空气柱的固有振动模式相匹配，就会发生共振，从而产生更响亮的声音。
对于两端开口的管子，也会发生类似现象。管内的空气柱在两端具有最大的空气位移，因此，在特定频率下，声波在每端的反射会产生大振幅的波。
两端开口管的共振频率遵循与两端固定的弦上的驻波相同的方程。
View the full transcript and gain access to JoVE Core videos
Q1: What is resonance in the context of sound waves?
Resonance occurs when a driving frequency matches an object's natural frequency, causing it to vibrate with significantly higher amplitude. For sound, this happens when a vibrating tuning fork's frequency matches an air column's normal modes. The result is a louder sound produced by the resonating air column.
Q2: How do boundary conditions affect resonance in tubes?
Boundary conditions determine where nodes and antinodes form in a tube. A tube closed at one end has a node at the closed end and an antinode at the open end, creating anti-symmetrical conditions. A tube open at both ends has antinodes at each end, producing symmetrical boundary conditions that affect which frequencies resonate.
Q3: Why does a tuning fork produce louder sound in a resonant tube?
When a tuning fork's frequency matches the air column's natural frequency, the incident sound wave reflects off the tube's closed end and combines with incoming waves. This constructive interference creates standing waves with large amplitudes, amplifying the sound significantly compared to non-resonant frequencies.
Q4: What is the difference between nodes and antinodes in a resonating tube?
A node is a fixed point where air molecules have minimal freedom to oscillate, typically occurring at closed tube ends. An antinode is a point of maximum air displacement, occurring at open tube ends. The arrangement of nodes and antinodes determines which frequencies resonate in the tube.
Q5: How do tubes open at both ends differ from tubes closed at one end in resonance?
Tubes open at both ends have symmetrical boundary conditions with antinodes at each end, allowing maximum air displacement at both openings. Tubes closed at one end have anti-symmetrical conditions with a node at the closed end and antinode at the open end. Both configurations produce resonance, but at different frequencies.
Q6: What happens to sound waves when they reflect inside a resonant tube?
Reflected sound waves travel in the opposite direction from incident waves while maintaining the same frequency and wavelength. When incident and reflected waves combine at the correct frequency, they create standing waves with large amplitudes. This constructive combination produces the loud resonant sound characteristic of resonance.
Q7: Why do only specific frequencies resonate in an air column?
An air column has only specific natural frequencies determined by its length and boundary conditions. Most frequencies interfere destructively and produce minimal vibration. Only frequencies matching the air column's normal modes create standing waves with constructive interference, resulting in resonance at those particular frequencies.