Wave Mechanics and Stationary Waves

A set of vocabulary flashcards focusing on concepts related to stationary waves, wave frequency, and the relationships between different parameters affecting wave behavior.

Stationary Wave

A wave that stores, but does not transfer, energy.

Formation of Stationary Waves

Occurs when two waves with the same wavelength traveling in opposite directions interfere and undergo superposition.

Node

A point of zero displacement in a standing wave where two waves in antiphase destructively interfere.

Antinode

A point of maximum displacement in a standing wave where two waves in phase constructively interfere.

Fundamental Frequency Arrangement

At its fundamental frequency, a standing wave has one central antinode and a single node at each end.

Vibration Generator

Apparatus used to generate a wave in a piece of string.

Bridge

A triangular prism-shaped object that alters the length of the oscillating region of the string.

Signal Generator Stabilization

The signal generator needs to be operated for several minutes to stabilize the frequency.

Counterweight or G-Clamp

Device added to the clamp stand to prevent it from toppling over during experiments.

String Length and Frequency Relationship

There is an inverse relationship: as string length increases, the frequency of the first harmonic decreases.

Mass per Unit Length Effect on the first harmonic

As mass per unit length increases, the frequency of the first harmonic decreases.

Tension Effect on Frequency

As tension in the string increases, the frequency of the first harmonic also increases.

How can String Tension be varied

Tension can be varied by attaching a mass hanger to the end of the string.

Safety Precautions for Mass Hangers

Never stand directly under a mass hanger; use a padded bucket below to catch falling masses.

Tension Calculation

T=mg

Measuring Mass per Unit Length

Measure the mass of a long piece of string and divide by the string’s length.

Advantage of Long String in Measurement

Lower percentage uncertainty in the measurement when using a longer piece of string.

Doubling Frequency Effect

Changing the frequency to double that of the first harmonic results in the string resonating in its second harmonic.

Wave Speed Equation

v = f𝜆, which expresses wave speed as the product of frequency and wavelength.

Wavelength in Fundamental Mode

Wavelength (𝜆) is equal to 2 times the length of the oscillating string (𝜆 = 2L).

What graph is plotted and how is wave speed determined from it

• Graph of 1/f against L

• Gradient of the graph will be 1/fL.

• Wave speed is given by 2fL for the fundamental mode so is given by 2/gradient.

Gradient of 1/f vs L Graph

The wave speed is given by 2fL, where f is frequency and L is length.