Properties of waves

The image shows a display of an oscilloscope which is measuring an alternating voltage. The time base is set at 0.1 s / division. The voltage scale (y‑sensitivity) is set at 0.5 V / division.

Which row of the table shows the correct amplitude and correct frequency?

Your answer

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 flute is a musical instrument made from a long tube that is open at both ends.

A stationary sound wave in the tube produces a musical note.

The lowest frequency note that a standard flute produces in air is 262 Hz.

The speed of sound in air at a temperature of 20 °C is 340 m s^–1.

Show that a standard flute has an approximate length of 0.65 m.

In an ideal gas, the speed v of sound is given by

where

is a dimensionless constant that depends on the gas

R is the molar gas constant

T is the absolute temperature

M is the molar mass of the gas.

The table below shows values of and M for both air and helium.

Gas		M / g mol–1
Air	1.40	29.0
Helium	1.67	4.00

The kinetic model of an ideal gas assumes that there are a large number of particles in rapid, random motion.

State two further assumptions for the kinetic model of an ideal gas.

A standard flute is placed inside a sealed chamber.

The chamber is filled with helium at a temperature of –10 °C.

Calculate the lowest frequency that the flute could produce inside the chamber.

A pulsar is a rapidly rotating neutron star that emits radio waves.

Describe the formation of a neutron star.

State one characteristic of a neutron star.

An astronomer uses a radio telescope to observe a pulsar.

The graph below shows the power that the telescope receives due to the radio waves from one full rotation of a pulsar.

By calculating the area between the curve and the horizontal axis, estimate the total energy received by the telescope in one full rotation of the pulsar.

The surface area of the telescope is about 3000 m². (ii)

The distance to the pulsar is about 300 pc.

By assuming that the radiation from the pulsar is emitted equally in all directions, estimate the total energy emitted in one full rotation.

A beam of sound of intensity I₀ is reflected off the surface of water. The amplitude of the reflected sound is the amplitude of the incident sound. What is the intensity of the reflected sound in terms of I₀?

D I₀

Your answer

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.

Describe, in terms of X-ray photons, the attenuation mechanism of Compton scattering.

Use the graph to determine the exposure time t for the total radiant energy incident per cm² at a depth of 1.0 cm to be 2.6 J.

Beyond x = 1.0 cm, the tissue has a larger attenuation coefficient than the value calculated in (i).

On Fig. 24.2, sketch the variation of I with x beyond x = 1.0 cm.

Describe the origin of the microwave background radiation.

The figure below shows how the intensity of the microwave background radiation varies with its wavelength .

The peak intensity is at a wavelength of 1.1 mm.

This spectrum of microwave background radiation changes with temperature according to Wien’s displacement law.

Suggest and explain how the spectrum might have looked in the distant past. You may draw on the figure to support your answer.

Calculate the energy of a photon which has a wavelength of 1.1 mm.

Estimate the number of photons of microwave background radiation incident per second on the back of your hand.

Assume that all emitted photons have the energy calculated in (ii), and that the back of your hand has a surface area of 150 cm².

number of photons per second =........ s^–1

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.

Define the time constant of a circuit containing a capacitor of capacitance C and a resistor of resistance R.

By drawing a suitable tangent to the graph in Fig. 6.3, calculate the maximum current in the resistor.

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 stationary sound wave formed in a tube is shown below.

The tube is closed at one end. The length of the tube is 3.5 m. The speed of sound is 340 m s^–1.

What is the frequency of the sound wave?

A 97 Hz

B 120 Hz

C 240 Hz

D 486 Hz

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

The normal frequency range of hearing for young people is from 20 Hz to 20 kHz.

Describe how you can use an oscilloscope, and other additional laboratory equipment, to determine the actual upper limit of the frequency range for a young person.

State one difference and one similarity between the oscillations of a stationary sound wave and a progressive sound wave.

You are provided with a ray-box, a semi-circular block of plastic and other normal laboratory equipment. The outline of the block is shown below.

Describe how you could measure the refractive index n of the block using the critical angle method. Draw on the diagram and label it to make your answer clear.

A high-energy X-ray photon interacts with an electron of an atom through the Compton effect.

Describe this effect.

The diagram below shows a beam of X-rays incident normally on some soft tissue.

The attenuation (absorption) constant of the soft tissue is 0.85 cm^–1. The intensity of the beam is 4.6 × 10³ W m^–2. There is a small cyst 2.1 cm from the surface of the soft tissue. The cross-sectional area of the cyst normal to the beam is 3.4 × 10^–4 m².

The beam is switched on for 30 s.

Calculate the X-ray energy incident on the cyst in a period of 30 s.

The attenuation coefficients of the cyst and the soft tissues in (b) were similar. This prevented imaging the cyst using a two-dimensional X-ray image.

Name a different X-ray technique that could be used to image the cyst. Explain the advantage of this technique.

The diagram below shows the oscilloscope trace for an electrical signal.

The time-base setting of the oscilloscope is 2 s cm⁻¹.

What is the frequency of the signal?

A 125 Hz

B 250 Hz

C 125 kHz

D 250 kHz

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.

Both the ISS and the astronauts inside it are in free fall.

Explain why this makes the astronauts feel weightless.

Calculate the value of the gravitational field strength g at the height of the ISS above the Earth.

=........ N kg^–1 g

Use the information in (b)(ii) and the data below to show that the root mean square (r.m.s.) speed of the air molecules inside the ISS is approximately 15 times smaller than the orbital speed of the ISS.

• molar mass of air = 2.9 × 10^–2 kg mol^–1

• temperature of air inside the ISS = 20 °C

The ISS has arrays of solar cells on its wings. These solar cells charge batteries which power the ISS. The wings always face the Sun.

Use the data below and your answer to (b)(ii) to calculate the average power delivered to the batteries.

• The total area of the cells facing the solar radiation is 2500 m².

• 7% of the energy of the sunlight incident on the cells is stored in the batteries.

• The intensity of solar radiation at the orbit of the ISS is 1.4 kW m^–2 outside of the Earth’s shadow and zero inside it.

• The ISS passes through the Earth’s shadow for 35 minutes during each orbit.

Calculate the frequency f of the transmitted wave.

The electromagnetic wave is caused by electrons oscillating in the transmitter aerial. Each electron oscillates with simple harmonic motion.

Calculate the maximum acceleration a_max of an electron which oscillates with an amplitude of 4.0 × 10^–6 m.

=........ m s^–2 a_max

Suggest why the diode in Fig. 5.1 is necessary for an ammeter to detect a signal at the receiver aerial.

This question is about waves.

The period of a progressive wave can be determined from Fig. 16.1. Add a correct label to

the horizontal axis so that the period can be found.

A progressive wave has wavelength , frequency f and period T.

Show that the speed v of the wave is given by the equation v = f.

Calculate the period T of the light wave.

The rays of light are in phase at the dashed line X.

Use your two answers above to state the phase difference in degrees between the light rays at Y.

Question 16 continues on page 12

Fig. 17.1 shows the variation with distance of the displacement of a stationary wave at time

The period of the wave is T.

On Fig. 17.1, sketch a graph to show the variation of the displacement at time t =

On Fig. 17.1, show the positions of all the nodes. Label each node N.

A small loudspeaker emits sound uniformly in all directions. The amplitude of the sound is 12 m at a distance of 1.5 m from the loudspeaker.

What is the amplitude of the sound at a distance of 4.5 m from the loudspeaker?

A 1.3 m

B 4.0 m

C 6.9 m

D 12 m

Your answer

17* A metal circular plate is rotated at a constant frequency by an electric motor. The plate has a small hole close to its rim. Fig. 17.1 shows an arrangement used by a student to determine the frequency of the rotating

A light-dependent resistor (LDR) and a fixed resistor of resistance 1.2 k are connected in series to a battery. The battery has e.m.f. 4.5 V and has negligible internal resistance. The potential difference V across the resistor is monitored using a data-logger.

Fig. 17.2 shows the variation of V with time t.

Use your knowledge and understanding of potential divider circuits to explain the shape of the graph shown in Fig. 17.2. Include in your answer the maximum and minimum values of the resistance of the LDR. Describe how the student can determine the frequency of the rotating plate.

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