Podcast
Questions and Answers
What is the phenomenon described in the text when the amplitude of a resultant wave is not constant in time?
What is the phenomenon described in the text when the amplitude of a resultant wave is not constant in time?
- Destructive interference
- Constructive interference
- Beat frequency (correct)
- Harmonic oscillation
What are the points in a standing wave where the amplitude is zero called?
What are the points in a standing wave where the amplitude is zero called?
- Peak points
- Wave centers
- Antinodes
- Nodes (correct)
How is the beat frequency calculated according to the information provided?
How is the beat frequency calculated according to the information provided?
- $ν_{beat} = ν_1 + ν_2$
- $ν_{beat} = ν_1 imes ν_2$
- $ν_{beat} = |ν_1 - ν_2|$
- $ν_{beat} = ν_1 - ν_2$ (correct)
Where do two travelling waves in opposite directions lead to the formation of a stationary wave pattern?
Where do two travelling waves in opposite directions lead to the formation of a stationary wave pattern?
In the context of beats of frequency 2 Hz, what are the frequencies of the two harmonic waves illustrated in Fig. 15.16?
In the context of beats of frequency 2 Hz, what are the frequencies of the two harmonic waves illustrated in Fig. 15.16?
If the beat frequency between two sitar strings playing the note 'Dha' decreases from 5 Hz to 3 Hz, what action was taken regarding the tension of string B?
If the beat frequency between two sitar strings playing the note 'Dha' decreases from 5 Hz to 3 Hz, what action was taken regarding the tension of string B?
In a standing wave, what are the points with the largest amplitude known as?
In a standing wave, what are the points with the largest amplitude known as?
What is a significant feature of stationary waves?
What is a significant feature of stationary waves?
What does an increase in tension of a string typically do to its frequency?
What does an increase in tension of a string typically do to its frequency?
What characterizes the possible wavelengths or frequencies of vibration in a system of stationary waves?
What characterizes the possible wavelengths or frequencies of vibration in a system of stationary waves?
How does the amplitude of a resultant wave behave when the term cos ωb t takes its limit at +1 or -1?
How does the amplitude of a resultant wave behave when the term cos ωb t takes its limit at +1 or -1?
In a system of stationary waves, what determines the normal modes of oscillation?
In a system of stationary waves, what determines the normal modes of oscillation?
What is the term used to describe the frequencies at which a string or air column vibrates with certain frequencies?
What is the term used to describe the frequencies at which a string or air column vibrates with certain frequencies?
When do beats arise in a system?
When do beats arise in a system?
What is the Doppler effect?
What is the Doppler effect?
Which of the following statements is true regarding a wave?
Which of the following statements is true regarding a wave?
What does the observed frequency of a sound wave depend on according to the text?
What does the observed frequency of a sound wave depend on according to the text?
How can wind be differentiated from a sound wave in air?
How can wind be differentiated from a sound wave in air?
Flashcards
Beat Frequency
Beat Frequency
The phenomenon where the amplitude of a resultant wave varies over time due to the interference of two waves with slightly different frequencies.
Nodes
Nodes
Points in a standing wave where the amplitude is always zero.
Beat Frequency Formula
Beat Frequency Formula
The calculation of beat frequency given by the difference between the frequencies of two waves: $ν_{beat} = ν_1 - ν_2$.
Boundary Conditions
Boundary Conditions
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Frequencies of Harmonic Waves
Frequencies of Harmonic Waves
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Increased Tension
Increased Tension
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Antinodes
Antinodes
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Stationary Waves
Stationary Waves
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Effect of Tension
Effect of Tension
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Natural Frequencies
Natural Frequencies
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Amplitude Behavior
Amplitude Behavior
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Normal Modes
Normal Modes
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Resonant Frequencies
Resonant Frequencies
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Origin of Beats
Origin of Beats
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Doppler Effect
Doppler Effect
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Energy Transfer in Waves
Energy Transfer in Waves
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Observed Frequency
Observed Frequency
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Wind vs. Sound Wave
Wind vs. Sound Wave
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Study Notes
Standing Waves
- There is no phase difference between oscillations of different elements of the wave.
- The string as a whole vibrates in phase with differing amplitudes at different points.
- The wave pattern is neither moving to the right nor to the left, hence, they are called standing or stationary waves.
- The amplitude is fixed at a given location but is different at different locations.
- Nodes are points at which the amplitude is zero, and antinodes are points at which the amplitude is the largest.
Normal Modes of Oscillation
- The boundary conditions constrain the possible wavelengths or frequencies of vibration of the system.
- The system cannot oscillate with any arbitrary frequency, but is characterized by a set of natural frequencies or normal modes of oscillation.
- For a stretched string fixed at both ends, the positions of nodes (where the amplitude is zero) are given by sin kx = 0, which implies kx = n π; n = 0, 1, 2, 3,...
Beats
- Beats arise when two waves having slightly different frequencies, ν1 and ν2, and comparable amplitudes, are superposed.
- The beat frequency is νbeat = ν1 – ν2.
- The amplitude of the resultant wave shows beats at a frequency of 2ωb = ω1 – ω2.
Musical Pillars
- The musical pillars of Nelliappar and several other temples in southern India are unique to the country and have no parallel in any other part of the world.
Doppler Effect
- The Doppler effect is a change in the observed frequency of a wave when the source (S) or the observer (O) or both move(s) relative to the medium.
- For sound, the observed frequency ν is given in terms of the source frequency νo by ν = vo (v + vs) / (v - vo).
Points to Ponder
- A wave is not motion of matter as a whole in a medium.
- In a wave, energy and not the matter is transferred from one point to the other.
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