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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?
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?
How is the beat frequency calculated according to the information provided?
How is the beat frequency calculated according to the information provided?
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?
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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?
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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?
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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?
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What is a significant feature of stationary waves?
What is a significant feature of stationary waves?
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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?
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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?
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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?
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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?
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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?
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When do beats arise in a system?
When do beats arise in a system?
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What is the Doppler effect?
What is the Doppler effect?
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Which of the following statements is true regarding a wave?
Which of the following statements is true regarding a wave?
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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?
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How can wind be differentiated from a sound wave in air?
How can wind be differentiated from a sound wave in air?
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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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Description
Test your knowledge about standing waves, where different points oscillate in phase with differing amplitudes at fixed locations. Learn about nodes, where the amplitude is zero and there is no motion.
