Superposition Starting Check · H2 Physics 9478

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Answer 9 short questions. It shows what to work on next and doesn't count towards mastery.

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Two points on a sinusoidal progressive wave are separated by λ/6 along the propagation direction. What is the smaller phase-difference magnitude at one instant?

6π rad
π/3 rad
π/6 rad
2π/3 rad

At one point, two waves produce instantaneous displacements +3.0 mm and −5.0 mm. What is the resultant displacement?

+8.0 mm
−8.0 mm
−2.0 mm
+2.0 mm

At the open end of an ideal resonant air column, which pair of conditions applies?

Displacement node and pressure node
Displacement antinode and pressure antinode
Displacement antinode and pressure node
Displacement node and pressure antinode

How is an ideal standing wave formed?

By continuous matter transfer between alternating nodes.
By superposition of equal-amplitude, equal-frequency waves travelling in opposite directions, producing fixed nodes and antinodes.
By a single progressive wave stopping at every crest.
By two waves of different frequencies travelling in the same direction.

A string fixed at both ends vibrates in its fundamental mode. How does its length L relate to wavelength?

L = 2λ
L = λ/2
L = λ/4
L = λ

In a Young double-slit experiment, slit separation is 0.40 mm, screen distance is 2.0 m and wavelength is 600 nm. What is the fringe separation?

3.0 mm
0.12 mm
0.75 mm
4.8 mm

Which source condition is essential for a stable two-source interference pattern?

Different frequencies whose phase difference changes continuously
One source much brighter but unrelated in phase
Sources that alternate and never overlap at the observation point
A constant phase difference between sources of the same frequency

Normally incident 600 nm light reaches a grating with 500 lines mm⁻¹. Find the slit spacing and the angle of its second-order maximum.

Spacing 2.00 mm; angle 0.034°
Spacing 2.00 μm; second-order angle 36.9°
Spacing 500 μm; angle 14.5°
Spacing 0.500 μm; no second order

For 500 nm light through a 0.200 mm slit, find the first-minimum angle. State how narrowing a gap toward a water wave’s wavelength affects diffraction, and use θR ≈ λ/b to estimate the Rayleigh limit for aperture width b = 0.200 mm.

First minimum 2.50 rad; diffraction occurs only when b<λ.
First minimum 0; Rayleigh resolution is independent of aperture.
First minimum ≈2.50 mrad; narrower comparable gap diffracts more; Rayleigh limit ≈2.50 mrad.
First minimum 0.400 rad; narrower gap diffracts less; Rayleigh limit 0.400 rad.

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This check needs JavaScript to record answers. The reviewed questions are listed below for study.

A time graph and a position graph show the same periodic wave. Which horizontal separations represent one complete cycle?

One period on the time graph and one wavelength on the position graph
One wavelength on both graphs
One period on both graphs
One amplitude on the time graph and one period on the position graph

Which operation correctly applies the principle of superposition?

Add intensities first and treat the sum as displacement.
Keep only the wave with the larger amplitude.
Multiply the two displacements to obtain the resultant.
Add the signed displacements each wave would produce at the same place and time.

Adjacent nodes in a standing-wave pattern are 0.18 m apart. What is the wavelength of each component wave?

0.090 m
0.18 m
0.72 m
0.36 m

At a displacement node of a standing wave on a string, what is true?

The displacement amplitude is always zero there.
The displacement amplitude is maximum there.
The point travels along the string at the wave speed.
The node drifts by half a wavelength each cycle.

A resonance tube has adjacent displacement nodes 0.34 m apart. If sound speed is 340 m s⁻¹, what is the frequency?

2000 Hz
500 Hz
250 Hz
1000 Hz

A string fixed at both ends has fundamental frequency 120 Hz. Which is its next allowed harmonic frequency?

180 Hz
360 Hz
240 Hz
60 Hz

Two identical sinusoidal waves overlap exactly in antiphase. What resultant does ideal superposition give?

Zero displacement at every point of complete overlap
Twice the amplitude because intensities always add
The original amplitude because one wave replaces the other
A wave with twice the frequency

A pipe closed at one end sounds its fundamental note. What is found at the closed end of the pipe?

A displacement node and a pressure antinode.
A displacement antinode and a pressure node.
A displacement node and a pressure node.
A displacement antinode and a pressure antinode.

A Young pattern has fringe spacing 1.5 mm. Moving the screen from 1.5 m to 2.5 m without other changes gives what new spacing?

0.90 mm
1.67 mm
3.75 mm
2.5 mm

Why may coherent waves with very unequal amplitudes produce low-contrast fringes?

At nominal minima the larger wave is not fully cancelled, so dark regions remain relatively bright.
Unequal amplitudes make the sources have different frequencies.
The larger wave prevents the principle of superposition from applying.
All maxima disappear because only equal amplitudes can interfere.

On a stretched string, an upward pulse of height 3.0 cm and a downward pulse of depth 1.0 cm travel towards each other. At the instant their peaks coincide at the same point, what is the string's displacement there?

+4.0 cm
0 cm
−2.0 cm
+2.0 cm

Normally incident light gives a third-order maximum at 48.6° with a 300 lines mm⁻¹ grating. Find the wavelength.

1.11 μm
7.50 μm
833 nm
278 nm

A telescope’s aperture width is doubled at fixed wavelength. Using θR ≈ λ/b, state the Rayleigh-limit factor and compare it with the small-angle first-minimum scale for a slit whose width is also doubled.

Both angles become zero only when aperture equals wavelength.
Rayleigh angle halves and resolution improves; the single-slit first-minimum scale also halves.
Rayleigh angle doubles and resolution worsens.
Rayleigh angle is unchanged but the first minimum doubles.

Check my progress

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About 10 minutes

Answer 9 questions. You'll see your score, the answers and explanations at the end. Your result can count towards your course progress.

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Answer 9 questions. You'll see your score, the answers and explanations at the end. A scheduled review counts towards your course progress only when it is due.

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Superposition Starting Check · H2 Physics 9478

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