Stationary waves - A-Level Physics

Summary

This video explains the concept of stationary waves, their formation, and key features. Stationary waves occur when two waves of the same frequency travel in opposite directions and interfere to create nodes (points of zero displacement) and antinodes (points of maximum displacement). The video covers the role of superposition, constructive and destructive interference, and introduces the concepts of harmonics, with varying numbers of loops and nodes. Additionally, it explains how the frequency of stationary waves relates to string length, tension, and mass per unit length. The phase relationships in stationary waves, including in-phase and anti-phase interactions, are also discussed.

Takeaways

• 😀 Stationary waves are formed when two waves of the same frequency travel in opposite directions in the same medium, creating nodes and antinodes.
• 😀 Superposition is the principle behind stationary waves, where waves reinforce each other (constructive interference) or cancel each other out (destructive interference).
• 😀 Nodes are points where there is no displacement, while antinodes are points of maximum displacement in a stationary wave.
• 😀 The first harmonic (fundamental frequency) has a single loop, while higher harmonics have multiple loops and more nodes/antinodes.
• 😀 The second harmonic has two loops with one node in the middle, while the third harmonic has three loops.
• 😀 The distance between adjacent nodes in a stationary wave is always half the wavelength of the wave.
• 😀 The wavelength of the first harmonic is half the length of the string, and each subsequent harmonic adds another half wavelength.
• 😀 The speed of the wave is the product of its frequency and wavelength, following the equation v = f * λ.
• 😀 The fundamental frequency can be calculated using the formula: f = (1/2L) * √(T/μ), where L is the string length, T is the tension, and μ is the mass per unit length.
• 😀 Changes in tension, length, or mass per unit length affect the frequency of the stationary waves: increasing tension doubles the frequency, while increasing the string length reduces the frequency.
• 😀 In a stationary wave, points between adjacent nodes are in phase, while points on opposite sides of a node are in antiphase, meaning they move in opposite directions.

Q & A

What is the key difference between stationary waves and progressive waves?

The key difference is that stationary waves have energy localized to specific points, with particles oscillating between zero and maximum displacement, whereas progressive waves involve particles moving in a continuous up-and-down motion, transferring energy across the medium.

How are stationary waves formed?

Stationary waves are formed when two waves traveling in opposite directions, in the same medium and with the same frequency, superpose. This results in the formation of nodes (points of no displacement) and antinodes (points of maximum displacement).

What is the principle of superposition in the context of stationary waves?

The principle of superposition states that when two waves meet, their displacements add together. If they are in phase, their amplitudes reinforce (constructive interference), and if they are out of phase, their amplitudes cancel each other out (destructive interference).

What are nodes and antinodes in a stationary wave?

Nodes are points where there is no displacement due to destructive interference, while antinodes are points where the displacement is maximum due to constructive interference.

What happens to the frequency of a stationary wave when the tension in the medium is increased by a factor of four?

If the tension is increased by a factor of four, the frequency of the stationary wave doubles, as the frequency is proportional to the square root of the tension.

How do stationary waves relate to sound waves and musical instruments?

Stationary waves are fundamental to the operation of musical instruments and sound waves, where the medium (such as air or string) vibrates to produce sound. The formation of standing waves on strings or in air cavities leads to specific frequencies that create musical tones.

What is the first harmonic in terms of stationary waves?

The first harmonic, or fundamental frequency, corresponds to a stationary wave with one loop (or antinode) and two nodes (at the ends of the medium), with the entire length of the medium representing half the wavelength.

How does the shape of a stationary wave change as its frequency is increased?

As the frequency increases, the number of loops (antinodes) increases. For example, at the second harmonic, there are two loops, and at the third harmonic, there are three loops. The wavelength decreases as the frequency increases.

How is the length of a string related to the fundamental frequency of a stationary wave?

The fundamental frequency is inversely related to the length of the string. If the length of the string increases, the frequency decreases, and vice versa.

What is the equation for calculating the fundamental frequency of a stationary wave on a string?

The equation for calculating the fundamental frequency of a stationary wave is: f = 1 / (2L) * sqrt(T / μ), where L is the length of the string, T is the tension, and μ is the mass per unit length of the string.