【People's Education Press】High School Physics: Elective Compulsory Course 1: Generation of Mechanical Waves: How Does Vibration Propagate?

Imagine a thrilling sports game where the audience spontaneously stands up and sits down, creating a wave that sweeps across the stands. No one leaves their seat, yet the wave travels all the way to the other end of the field. This is preciselymechanical wavethe most intuitive illustration: the transmission of vibration through space.

1. Origin of Generation: Vibration and Interaction

The creation of a mechanical wave requires two 'partners':wave sourceandelastic medium. When the source particle oscillates under force, it pulls adjacent particles through interparticle interaction forces. This transfer of force does not happen instantaneously but spreads outward in layers asforced vibration.

When the driving frequency exactly matches the natural frequency of a particle, its amplitude reaches an astonishing maximum—this phenomenon is known asresonance (Resonance). The formula is expressed as:
$$\text{When } f_{drive} = f_0, \ A = A_{max}$$

2. Microscopic Determination of Simple Harmonic Motion

For a pendulum with small-angle oscillations (where $\widehat{AB} \ll R$), the restoring force is proportional to displacement: $F = -mg \sin\theta \approx -mg \frac{x}{l}$. This confirms the motion is simple harmonic, and its natural frequency depends on the length:
$$f_0 = \frac{1}{2\pi}\sqrt{\frac{g}{l}}$$

Core Observation

Particles Do Not Travel with the Wave: If you tie a red ribbon to a rope, you’ll notice it only vibrates up and down in place, never reaching the end. What propagates is the 'form' of the vibration and energy.

QUESTION 1

What are the two essential conditions for generating a mechanical wave?

Wave source and vacuum environment

Wave source and elastic medium

Driving force and vacuum environment

Fixed frequency and infinite space

QUESTION 2

How do particles in a medium move during the propagation of a mechanical wave?

Move forward with the waveform

Perform forced vibrations near their equilibrium positions

Remain constantly stationary

QUESTION 3

What phenomenon occurs when the driving frequency equals an object’s natural frequency?

Vibration stops

Interference occurs

Resonance occurs, and amplitude reaches its maximum

QUESTION 4

As shown in Figure 2.6-7, three small balls A, B, and C are suspended from a taut horizontal rope... Let ball A swing perpendicularly to the rope. What will be observed about balls B and C in the initial period?

B and C remain stationary

B and C begin to swing, and their frequency eventually matches that of ball A

B and C swing at their own natural frequencies

QUESTION 5

Figure 2.6-8 shows the resonance curve of a pendulum. If the pendulum length increases, how will the horizontal coordinate corresponding to the maximum amplitude change?

Moves to the right (frequency increases)

Does not change

Moves to the left (frequency decreases)