Superposition

Light waves are emitted from two sources.
What is a necessary condition for observable interference fringes to be produced?

Options

A   The waves must be polarised.
B   The waves must not be polarised.
C   The waves must be coherent.
D   The waves must have equal amplitudes.

The diagram shows a water wave in a shallow tank. The wave is diffracted through a gap in a barrier and spreads. The wavelength of the wave is much smaller than the width of the gap.

The wavelength of the wave and the width of the gap are both changed by a small amount.
Which combination of changes must increase the amount of spreading due to diffraction?

Options

Light of wavelength $567\text{ nm}$ is incident normally on a diffraction grating. The grating has $400$ lines per mm. A number of diffraction maxima are observed on the far side of the grating.
What is the angle between the second-order maximum and the third-order maximum?

Options

A   $13.1^\circ$
B   $13.9^\circ$
C   $15.9^\circ$
D   $27.0^\circ$

One wave has an amplitude of $2A$. A second wave has an amplitude of $\dfrac{A}{2}$. The waves are otherwise identical.

The two waves travel in opposite directions and overlap.

What is the ratio $\dfrac{\text{minimum amplitude of combined wave}}{\text{maximum amplitude of combined wave}}$?

Options

A   $\dfrac{2}{3}$
B   $\dfrac{3}{5}$
C   $\dfrac{2}{5}$
D   $4$

Light of wavelength $680\text{ nm}$ is incident normally on a diffraction grating with $450$ lines $\text{mm}^{-1}$.

What is the angle of diffraction of the second-order maximum in the diffraction pattern that is produced?

Options

A   $1.8^\circ$
B   $3.5^\circ$
C   $18^\circ$
D   $38^\circ$

A hollow tube is closed at one end and open at the other.

A stationary sound wave of the lowest possible frequency, $820\text{ Hz}$, is produced in the tube.

The speed of sound in air is $330\text{ m s}^{-1}$.

What is the length of the tube?

Options

A   $10\text{ cm}$
B   $20\text{ cm}$
C   $40\text{ cm}$
D   $160\text{ cm}$

A teacher removes the turntable from a microwave oven and places a bar of chocolate in the oven. She then switches the oven on for a short time.

A stationary wave is formed in the oven.

When the chocolate is removed, the teacher observes that there are two small sections of melted chocolate $6.0\text{ cm}$ apart with unmelted chocolate in between.

Each section of melted chocolate is located at an antinode.

Assume that the speed of the microwaves is $3.0 \times 10^8\text{ m s}^{-1}$.

What is the frequency of the microwaves emitted by the oven?

Options

A   $25\text{ MHz}$
B   $50\text{ MHz}$
C   $2.5\text{ GHz}$
D   $5.0\text{ GHz}$

A student uses a diffraction grating to determine the wavelength of visible light from a source.

The diffraction grating has $300$ lines per mm. The student measures the angle $\theta$ of each order $n$ of the intensity maxima. A graph of $n$ against $\sin \theta$ is plotted. The line of best fit for the plotted points is shown and has gradient $G$.

Which expression represents the wavelength, in m, of the visible light in terms of $G$?

Options

A   $3 \times 10^5 G$
B   $3.3 \times 10^{-6} G$
C   $\dfrac{3.3 \times 10^{-6}}{G}$
D   $\dfrac{300}{G}$

Two waves meet.

What is not a necessary condition for the waves to produce a stationary wave?

Options

A   They must be of the same type.
B   They must have the same period.
C   They must have the same wavelength.
D   They must travel in the same direction.

Light of a single wavelength is incident normally on a double slit. Interference fringes are observed on a screen.

The distance from the double slit to the screen is $0.60\text{ m}$ and the fringe separation is $1.8\text{ mm}$.

The distance from the double slit to the screen increases by $0.90\text{ m}$.

What is the new fringe separation?

Options

A   $1.2\text{ mm}$
B   $2.7\text{ mm}$
C   $4.5\text{ mm}$
D   $5.4\text{ mm}$