Question:medium
Which of the following conditions will lead to Anomalous dispersion?
Which of the following conditions will lead to Anomalous dispersion?
Show Hint
A simple way to remember is:
- Normal: \(v_g<v_p\) (The "normal" situation for light through a prism).
- Anomalous: \(v_g>v_p\) (The "anomalous" or unusual case).
- Non-dispersive: \(v_g = v_p\) (e.g., light in a vacuum).
Updated On: Feb 10, 2026
- Group velocity>Phase Velocity
- Group velocity<Phase Velocity
- Group velocity = Phase Velocity
- Doesn't depend on relation of group and phase velocity
Show Solution
The Correct Option is A
Solution and Explanation
Step 1: Establish the definition of dispersion. Dispersion is the effect where a wave's phase velocity is dependent on its frequency. This relationship is described by the group velocity (\(v_g = \frac{d\omega}{dk}\)) and the phase velocity (\(v_p = \frac{\omega}{k}\)).
Step 2: Classify the different types of dispersion.
- No Dispersion: Phase velocity remains constant across all frequencies, resulting in \(v_g = v_p\).
- Normal Dispersion: Phase velocity diminishes as frequency rises, observed in materials like glass for light. This condition is met when \(v_g<v_p\).
- Anomalous Dispersion: Phase velocity escalates with increasing frequency. This typically occurs near a medium's absorption frequency and is characterized by \(v_g>v_p\).
Consequently, anomalous dispersion is present when the group velocity exceeds the phase velocity.
Step 2: Classify the different types of dispersion.
- No Dispersion: Phase velocity remains constant across all frequencies, resulting in \(v_g = v_p\).
- Normal Dispersion: Phase velocity diminishes as frequency rises, observed in materials like glass for light. This condition is met when \(v_g<v_p\).
- Anomalous Dispersion: Phase velocity escalates with increasing frequency. This typically occurs near a medium's absorption frequency and is characterized by \(v_g>v_p\).
Consequently, anomalous dispersion is present when the group velocity exceeds the phase velocity.
Was this answer helpful?
1
Top Questions on Waves
- Two coherent loudspeakers \(L_1\) and \(L_2\) are placed at a separation of \(10\,\text{m}\) parallel to a wall at a distance of \(40\,\text{m}\) as shown in the figure. On a width \(AB\) on the wall, 10 maxima and minima are found. If the velocity of sound is \(324\,\text{m s}^{-1}\), find the frequency of sound. (Given: \( \sqrt{5}=2.23 \)).
- The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is \( \frac{5}{x} \). The value of \( x \) is ________.
- In an open organ pipe \( \nu_3 \) and \( \nu_6 \) are 3rd and 6th harmonic frequencies, respectively. If \( \nu_6 - \nu_3 = 2200\ \text{Hz} \), then the length of the pipe is _________ mm. (Take velocity of sound in air as \(330\ \text{m s}^{-1}\).)
Two loudspeakers (\(L_1\) and \(L_2\)) are placed with a separation of \(10 \, \text{m}\), as shown in the figure. Both speakers are fed with an audio input signal of the same frequency with constant volume. A voice recorder, initially at point \(A\), at equidistance to both loudspeakers, is moved by \(25 \, \text{m}\) along the line \(AB\) while monitoring the audio signal. The measured signal was found to undergo \(10\) cycles of minima and maxima during the movement. The frequency of the input signal is _____________ Hz.
(Speed of sound in air is \(324 \, \text{m/s}\) and \( \sqrt{5} = 2.23 \))
- Want to practice more? Try solving extra ecology questions todayView All Questions