Wave Interference and Standing Waves - AP Physics 2

First overtone frequency is $440 \text{ Hz}$. First overtone is the second harmonic: $f_2 = 2f_1$.

Wave speed $v = 250 \text{ m/s}$. Using $v = f\lambda = 50 \times 5 = 250$ m/s.

Wave speed $v = 300 \text{ m/s}$.. Using $v = f\lambda = 100 \times 3 = 300$ m/s.

Increased tension increases wave speed. Higher tension provides greater restoring force, increasing wave speed.

First overtone frequency is $440 \text{ Hz}$. First overtone is the second harmonic: $f_2 = 2f_1$.

The net displacement is the sum of individual displacements. This describes wave superposition where effects combine algebraically.

Wave speed decreases by factor of $\frac{1}{\sqrt{2}}$. Wave speed is proportional to $\sqrt{T}$, so halving tension reduces speed.

$f_n = n\frac{v}{2L}$, $n = 1, 2, 3, \text{...}$. Each harmonic is an integer multiple of the fundamental frequency.

Intensity is proportional to $A^2$. Wave energy is proportional to amplitude squared.

A wave that appears to be stationary, with nodes and antinodes. Formed by two waves traveling in opposite directions interfering.

Third harmonic $f_3 = 510 \text{ Hz}$. Using $f_3 = 3f_1 = 3 \cdot \frac{340}{2} = 510$ Hz.

Damping reduces wave amplitude over time. Energy dissipation causes gradual decay of oscillation amplitude.

String length, tension, and mass per unit length. These parameters determine the fundamental frequency and harmonics.

Phase difference of $\text{\textit{π}}$ radians. Antiphase means waves are exactly out of phase by half cycle.

Inversely proportional: $f \text{\textit{λ}} = v$.. Higher frequency means shorter wavelength for constant wave speed.

Neither complete constructive nor destructive interference. Partial interference occurs with phase differences between 0 and $\pi$.

Wave speed depends on the medium's properties. Wave speed is independent of frequency for a given medium.

Phase difference is $0$ or $2\text{\textit{π}}$ radians. Waves oscillate in perfect synchronization.

$v = f\text{\textit{λ}}$, where $f$ is frequency, $\text{\textit{λ}}$ is wavelength. Fundamental relationship between wave properties.

Wave speed $v = 250 \text{ m/s}$. Using $v = f\lambda = 50 \times 5 = 250$ m/s.

$f_2 = 170 \text{ Hz}$.. Second harmonic: $f_2 = 2f_1 = 2 \cdot \frac{340}{4} = 170$ Hz.

Path difference is an odd multiple of $\frac{\text{\textit{λ}}}{2}$. Waves arrive out of phase when path difference is half-wavelengths.

Path difference is a multiple of the wavelength, $n \lambda$. Waves arrive in phase when path difference equals whole wavelengths.

Wave speed $v = 300 \text{ m/s}$.. Using $v = f\lambda = 100 \times 3 = 300$ m/s.

Wavelength $\text{\textit{λ}} = 2 \text{ m}$. Using $\lambda = \frac{v}{f} = \frac{340}{170} = 2$ m.

$f_1 = 300 \text{ Hz}$. Using $f_1 = \frac{v}{2L} = \frac{300}{2 \times 0.5} = 300$ Hz.

Nodes are points of no displacement; antinodes have maximum displacement. Nodes and antinodes are separated by $\frac{\lambda}{4}$.

The frequency of the wave remains unchanged. Standing waves maintain constant frequency as amplitude varies spatially.

Nodes at fixed boundaries; antinodes at open boundaries. Boundary conditions determine the standing wave pattern.