Standing Waves Questions: Quiz and Flashcards

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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?

Destructive interference

Constructive interference

Beat frequency (correct)

Harmonic oscillation

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?

$ν_{beat} = ν_1 + ν_2$

$ν_{beat} = ν_1 imes ν_2$

$ν_{beat} = |ν_1 - ν_2|$

$ν_{beat} = ν_1 - ν_2$ (correct)

Where do two travelling waves in opposite directions lead to the formation of a stationary wave pattern?

Boundary conditions Signup and view all the answers

In the context of beats of frequency 2 Hz, what are the frequencies of the two harmonic waves illustrated in Fig. 15.16?

11 Hz and 9 Hz Signup and view all the answers

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?

Increased tension in string B Signup and view all the answers

In a standing wave, what are the points with the largest amplitude known as?

Antinodes Signup and view all the answers

What is a significant feature of stationary waves?

Constrained possible wavelengths Signup and view all the answers

What does an increase in tension of a string typically do to its frequency?

Increases the frequency Signup and view all the answers

What characterizes the possible wavelengths or frequencies of vibration in a system of stationary waves?

Natural frequencies Signup and view all the answers

How does the amplitude of a resultant wave behave when the term cos ωb t takes its limit at +1 or -1?

Increases Signup and view all the answers

In a system of stationary waves, what determines the normal modes of oscillation?

Boundary conditions Signup and view all the answers

What is the term used to describe the frequencies at which a string or air column vibrates with certain frequencies?

Resonant frequencies Signup and view all the answers

When do beats arise in a system?

When two waves have slightly different frequencies Signup and view all the answers

What is the Doppler effect?

A change in the frequency of a wave Signup and view all the answers

Which of the following statements is true regarding a wave?

Energy is transferred from one point to another Signup and view all the answers

What does the observed frequency of a sound wave depend on according to the text?

The source frequency and relative velocities of source and observer Signup and view all the answers

How can wind be differentiated from a sound wave in air?

Wind involves motion of air while sound involves motion of matter Signup and view all the answers

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.

Standing Waves and Nodes Quiz