How are standing waves created?

Standing waves are formed when two sets of waves with the same amplitude and wavelength travel in opposite directions and interfere with each other, typically due to reflection.

How does Milder's experiment demonstrate wave properties?

Milder's experiment uses a string with varying tension (weights) to show how wave speed changes. Faster waves (higher tension) result in shorter wavelengths and different patterns of nodes and loops.

Resonance is the phenomenon where a vibrating body can be set into high amplitude vibration by applying external pushes at its natural frequency.

Why might a grandfather clock stop on Thursday?

By Thursday, the descending weights in an 8-day clock are positioned such that their slight movement can pick up energy from the pendulum, causing it to miss a beat and stop, unless the clock is very firmly fixed.

Key Moments

Waves and Vibrations - with Sir Lawrence Bragg

Royal Institution

Science & Technology4 min read21 min video

Oct 24, 2016|50,547 views|1,663|40

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Key Moments

TL;DR

Sir Lawrence Bragg explains waves, vibrations, reflection, Doppler Effect, and resonance using demonstrations.

Key Insights

Waves are a transfer of displacement through a medium, not the movement of the medium itself.

Standing waves are formed by the superposition of two waves traveling in opposite directions.

The relationship between wave velocity, wavelength, and frequency is fundamental (velocity = wavelength x frequency).

Resonance occurs when a system is driven at its natural frequency, leading to amplified vibrations.

The Doppler Effect explains the change in frequency of a wave relative to an observer due to relative motion.

Even everyday objects like grandfather clocks can exhibit complex vibrational phenomena like linked pendulums.

DEMONSTRATING THE NATURE OF WAVES

Sir Lawrence Bragg begins by illustrating the fundamental difference between a vibration and a wave. A vibration is the back-and-forth motion of an object, like a weight on a spring. A wave, however, is the propagation of this disturbance through a medium. Using a long steel tape with attached rods, he shows that if one rod is held fixed, the others can vibrate. But when the support is removed, displacing one rod causes a ripple effect, transferring the displacement along the tape – this is a wave. A more sophisticated model, the "vinome" model, further clarifies this, demonstrating how a displacement travels along a series of linked elements without them permanently moving from their positions.

REFLECTION AND STANDING WAVES

The lecture then explores wave reflection. When waves traveling through a medium reach a boundary, they are reflected back. Bragg demonstrates this phenomenon, particularly focusing on the creation of standing waves. By superimposing two sets of waves of equal amplitude and wavelength traveling in opposite directions, he shows how their effects can add up or cancel out at different points in time. This interference pattern results in what are known as standing waves, characterized by fixed points of no displacement (nodes) and maximum displacement (loops).

THE PHYSICS OF STANDING WAVES

The formation of standing waves is explained through the principle of superposition. Bragg uses diagrams to illustrate how two waves moving towards each other interact. At certain points, crests align with crests and troughs with troughs, resulting in large displacements. At other points, crests align with troughs, leading to cancellation and minimal displacement. The visible outcome is a wave pattern that appears to oscillate in place, with fixed nodes and antinodes. The wavelength of the original traveling waves is shown to be twice the distance between two consecutive nodes or antinodes in the resulting standing wave.

RELATIONSHIP BETWEEN WAVE VELOCITY, WAVELENGTH, AND FREQUENCY

Bragg delves into the crucial relationship between wave velocity, wavelength, and frequency. He uses sound waves and Mildred's experiment with a vibrating string as examples. By altering the tension (weight) on the string, the wave velocity changes, affecting the number of nodes and loops (standing waves) visible for a constant vibration frequency. Conversely, using a tube with gas and jets, he demonstrates how changing the frequency of the oscillator alters the number of nodes and loops while the wave velocity remains constant, resulting in a change in pitch (octave). This reinforces the formula: velocity = wavelength × frequency.

PRINCIPLES OF RESONANCE

A significant portion of the talk is dedicated to resonance, the phenomenon where a system vibrates with maximum amplitude when driven by an external force at its natural frequency. Bragg illustrates this with rods of matched frequencies – vibrating one causes its twin to resonate and vibrate. He draws a parallel to tuning a radio, where the set's oscillation frequency is matched to the broadcast station's frequency. A more complex model demonstrating the ear's function further exemplifies resonance, as various 'tremblers' respond to different frequencies generated by a vibrating flywheel.

LINKED VIBRATIONS AND PRACTICAL EXAMPLES

Finally, Bragg explores the concept of linked vibrations using two pendulums of the same length suspended from a movable platform. Energy is transferred between the pendulums as one's vibration influences the other's support. This energy exchange leads to alternating periods of swinging and near-stillness for each pendulum. He provides a fascinating, albeit anecdotal, explanation for why grandfather clocks supposedly stop on Thursdays: by Thursday, the descending weights can be positioned such that their slight movement due to the pendulum's swing can cause the pendulum to miss a beat, especially if the clock is not firmly secured to the wall.

Mentioned in This Episode

●Studies Cited

Key Concepts in Waves and Vibrations

Practical takeaways from this episode

Do This

Observe how displacement propagates through a medium as a wave.

Understand that standing waves are formed by the superposition of two waves moving in opposite directions.

Recognize resonance occurs when a vibrating body is pushed at its natural frequency.

Fix grandfather clocks firmly to the wall to prevent weights from disrupting the pendulum.

Tune radio sets so oscillations match the frequency of the desired station for clear reception.

Avoid This

Do not consider a single vibrating pendulum as a fundamental vibration in a coupled system.

Avoid letting weights in a grandfather clock interfere with the pendulum's swing, especially by Thursday.

Common Questions

A vibration is the back-and-forth motion of a single object. A wave is the propagation of this disturbance through a medium, where the motion is transferred from one point to the next.