Interference and Young's double slit

Explain these observations.

The distance between the centres of X and Y is 70.0 cm, the distance D (as shown in the diagram) is 4.00 m and the distance from P₁ to P₂ is 1.25 m.

Use the two source interference formula to calculate the frequency of the sound waves. (Speed of sound = 340 m s^–1)

Loudspeaker Y is now replaced with a loudspeaker that produces sound waves of twice the original amplitude.

Describe how the signal observed on the oscilloscope varies as the microphone is moved along the line P₁ to P₃.

Explain what is meant by the term intensity.

Calculate the factor by which the intensity of the sound waves at P₁ in (c) is larger than the intensity of the original sound waves at P₁.

A graph of displacement s against distance x for a progressive wave at time t = 0 is shown

Determine:

the phase difference in radians between the points on the wave at x = 1.5 cm and x = 2.5 cm

the displacement s at time t = T at x = 1.5 cm, where T is the period of the oscillations of the wave.

A student is doing an experiment to determine the speed of sound in air by producing stationary waves inside a horizontal glass tube.

Fine powder is sprinkled inside the tube. A loudspeaker is placed close to the open end of the tube. The other end of the tube is closed. The loudspeaker is connected to a signal generator producing a frequency of 2.72 kHz. The powder inside the tube forms piles at certain locations inside the tube, see Fig. 16.2.

Suggest why the powder piles up at the nodes within the tube.

Determine the fundamental (minimum) frequency f₀ of the stationary wave that can be formed within this tube.

A student experiments with microwaves emitted from a transmitter. The frequency f of the microwaves from the transmitter can be adjusted.

The microwaves are produced by an alternating current in the transmitter.

In one experiment, f is 11 GHz. In a wire in the transmitter, the magnitude of the maximum alternating current is 20 mA. The wire has cross-sectional area 1.4 × 10^–8 m² and is made of a metal with free electron number density 8.0 × 10²⁸ m^–3.

The student models the average motion of the free electrons in the wire as simple harmonic motion.

Use your answer to (i) to calculate the amplitude A of this motion.

Without further calculation, explain how the maximum acceleration of a free electron varies as the frequency f is adjusted, provided that the maximum alternating current remains constant.

The student connects two microwave transmitters X and Y, and places them in front of a microwave detector D, as shown in the diagram below.

The transmitters X and Y produce coherent vertically polarised microwaves with the same frequency f.

The detector D is sensitive to vertically polarised microwaves only.

When the detector D is moved along the line PQ, a pattern of maximum and minimum intensity is observed. Adjacent maxima are separated by a distance x.

* Explain:

• why this pattern of intensity occurs

• the expected relationship between the frequency f and the distance x

• how to verify this relationship experimentally.

Monochromatic light from a laser is incident normally on a diffraction grating. A series of bright dots are formed on a distant screen.

Which two terms can be used to explain these bright dots?

A diffraction, interference

B reflection, interference

C refraction, diffraction

D refraction, reflection

Your answer

A double-slit is used in an interference experiment to independently investigate the light from two sources K and L. The light from the sources have different wavelengths. The table below shows some data.

Light source	Wavelength of light	Separation between adjacent bright fringes	Distance between screen and double‑slit
K		1.2 mm	D
L	0.80		0.50D

What is the separation between adjacent bright fringes for source L?

A 0.48 mm

B 1.2 mm

C 1.9 mm

D 3.0 mm

Your answer

The diagram below shows the graphs of displacement x against time t for two waves S and T.

The waves meet at a point in space. The superposition of these two waves produces a resultant wave.

What is the frequency f and the amplitude A of the resultant wave?

A f = 100 Hz, A = 2.0 mm

B f = 100 Hz, A = 4.0 mm

C f = 200 Hz, A = 2.0 mm

D f = 200 Hz, A = 4.0 mm

Your answer

A sound wave is incident at the ear.

The amplitude of the sound wave is 7.8 nm. The intensity of the sound at the earhole is 4.8 × 10⁻⁷ W m⁻².

Determine the power of the sound incident at the earhole by estimating the diameter of the earhole in mm.

diameter of earhole ≈........ mm

A different sound wave is now incident at the ear. The intensity of this wave is 9.6 × 10⁻⁷ W m⁻².

Calculate the amplitude A in nm of this sound wave.

State the principle of superposition.

The diagram below shows monochromatic light from a laser incident normally at a double-slit.

The diagram is not drawn to scale.

A small light-detector is mounted onto a trolley on a frictionless track. The trolley travels along the track at a constant speed.

The separation between the slits is 0.20 mm. The perpendicular distance between the slits and the track is 8.2 m.

A series of bright and dark fringes are detected at the moving light-detector.

Explain, in terms of phase difference, the origin of the fringes.

Coherent radio waves from transmitters X and Y are emitted in phase. The waves interfere constructively at point Z.

The distance XZ is 16.0 m and the distance YZ is 20.0 m. The radio waves have wavelength .

Which value of is not possible?

A 1.0 m

B 2.0 m

C 3.0 m

D 4.0 m

Your answer

Fig. 19.1 shows the image from an experiment using a ripple tank.

A straight ruler repeatedly hits the surface of water. Waves on the surface of the water travel in the direction shown by the two large upward white arrows. The waves are incident at a solid barrier.

Closely examine the image shown in Fig. 19.1.

State two wave phenomena (properties) that can be observed in this image. You may annotate Fig. 19.1 to support your answer.

A progressive wave of amplitude a has intensity I. This wave combines with another wave of amplitude 0.6 a at a point in space. The phase difference between the waves is 180°.

What is the resultant intensity of the combined waves in terms of I ?

A 0.16 I

B 0.4 I

C 1.6 I

D 2.6 I

Your answer

State the principle of superposition of waves.

Fig. 16.1 shows an arrangement to demonstrate the interference of monochromatic light.

Coherent blue light from a laser is incident at a double-slit. The separation between the slits is 0.25 mm. A series of dark and bright lines (fringes) appear on the screen. The screen is 4.25 m from the slits. Fig. 16.2 shows the dark and bright fringes observed on the screen.

The pattern shown in Fig. 16.2 is drawn to scale.

Use Fig. 16.2 to determine accurately the wavelength of the blue light from the laser.

The blue light is now replaced by a similar beam of red light. State and explain the effect, if any, on the fringes observed on the screen.