Waves — practice questions

A wave has a period of $0.020$ s.

Calculate its frequency.

On a displacement–distance graph of a water wave, the vertical distance from a trough to a crest is $8.0$ cm, and the distance from one crest to the next is $60$ cm. Twenty waves pass a post in $5.0$ s.

State the amplitude, wavelength and frequency of the wave, and explain how the amplitude is found from the graph.

A student says: "A water wave carries the water from the middle of the lake to the shore, and a bigger wave carries it faster."

Discuss this statement. Your answer should explain what a wave actually transfers, how the particles of the medium move, and what amplitude and frequency each control.

A wave has a frequency of $12$ Hz and a wavelength of $0.25$ m.

Calculate its speed.

Water waves of wavelength $0.30$ m travel at $1.2$ m s⁻¹ in deep water. They pass into a shallow region where their speed drops to $0.80$ m s⁻¹.

Calculate the wavelength in the shallow water, and explain why the frequency is the same in both regions.

A red laser beam of wavelength $650$ nm in air ($v = 3.0 \times 10^8$ m s⁻¹) enters a glass block in which its speed is $1.9 \times 10^8$ m s⁻¹.

Calculate the frequency and the wavelength in the glass. Then explain fully why the light does not change colour inside the glass, and what an observer would notice about the beam's direction as it enters.

A ray of light strikes a plane mirror with an angle of incidence of $38°$.

State the angle of reflection, and state what the angle is measured from.

A pulse travels along a rope toward an end that is tied firmly to a post, and reflects.

Describe what happens to the pulse on reflection, and explain what happens to its speed and wavelength.

Two identical pulses travel toward the ends of a long spring at the same speed. The left end is tied firmly to a wall; the right end is attached to a light ring that can slide freely up and down a smooth vertical pole.

Compare what happens to each pulse on reflection. Explain fully why the two behave differently, and explain what stays the same in both cases.

Water waves slow down as they move from deep water into shallow water at an angle to the boundary.

State which way the waves bend, and state what happens to their wavelength.

Light travelling in air enters a glass block at an angle to the normal and slows down.

Explain why the light changes direction at the surface, and state what happens to its frequency and wavelength.

Ocean waves approach a straight beach at an angle of about $40°$ to the shoreline, yet by the time they break they are almost exactly parallel to the shore.

Explain fully why this happens. In your answer refer to how the water depth affects wave speed, and to what happens to the wavelength, frequency and direction of the waves as they approach.

Two crests, one of amplitude $3.0$ cm and one of amplitude $5.0$ cm, meet at the same point on a rope.

Calculate the resultant displacement at that point, and state whether this is constructive or destructive superposition.

A crest of amplitude $5.0$ cm meets a trough of amplitude $5.0$ cm on a rope.

Describe what the rope looks like at the moment they exactly overlap, and describe what happens to the two pulses immediately afterwards. Explain your answer.

A student watches two identical but opposite pulses meet on a long spring. At one instant the spring is completely flat along its whole length.

The student concludes that the energy of the two pulses has been destroyed. Discuss this conclusion fully, explaining where the energy actually is at that instant and how you know.

Water waves pass through a gap in a barrier and spread out on the far side.

Name this effect, and state what happens to the wavelength of the waves as they pass through the gap.

Water waves of wavelength $2.0$ cm pass through a gap $2.0$ cm wide, and then through a second gap $10$ cm wide.

Describe and explain the difference in the diffraction pattern produced by the two gaps.

A person stands in a corridor around the corner from an open classroom door. They can clearly hear the teacher talking but cannot see into the room at all.

Explain fully why sound behaves so differently from light here. Include an estimate of the relevant wavelengths, and explain why this does not mean that light fails to diffract.

Two coherent sources produce an interference pattern in a ripple tank.

State what is observed along an antinodal line, and state the condition on the path difference for a point to lie on one.

Two dippers in a ripple tank vibrate in phase at the same frequency, producing an interference pattern.

Explain why the line running directly midway between the two dippers is always an antinodal line, and describe what happens to the spacing of the pattern if the frequency of both dippers is increased.

Two loudspeakers a few metres apart are connected to the same signal generator producing a single steady note. A student walking in a line across the room in front of them hears the sound rise and fall in loudness repeatedly.

Explain fully why this happens, and predict and explain what the student would notice if (a) the note were changed to a lower frequency and (b) the speakers were moved further apart. Address what happens to the sound energy at the quiet positions.

Light travels from air into a glass block of refractive index $1.5$ with an angle of incidence of $30°$.

Calculate the angle of refraction.

Light passes from water ($n = 1.33$) into air with an angle of incidence of $35°$.

Calculate the angle of refraction, and explain why the ray bends away from the normal in this case.

A narrow beam of light in air strikes one face of a rectangular glass block ($n = 1.52$) at an angle of incidence of $45°$, passes through the block, and emerges from the opposite, parallel face.

Calculate the angle of refraction inside the block and the angle at which the light emerges. Explain fully why the emerging beam is parallel to the original beam, and describe what else has changed about the light while it was inside the glass.

A material has a refractive index of $1.60$.

Calculate the critical angle for a boundary between this material and air.

A ray of light inside a water tank ($n = 1.33$) strikes the water–air surface at an angle of incidence of $55°$.

Calculate the critical angle for water and air, and explain what happens to the ray.

An optical fibre has a glass core of refractive index $1.50$.

Calculate the critical angle at the core–air boundary. Explain fully how the fibre keeps light travelling along its length, and explain why total internal reflection is used rather than coating the inside of the fibre with a mirror. Comment on what would happen if the fibre were bent very sharply.

A ray of light travelling parallel to the principal axis strikes a converging lens.

State the path of the ray after it passes through the lens.

An object is placed between $F$ and $2F$ in front of a converging lens.

Describe the image formed, giving its nature, orientation and size, and explain how a ray diagram shows the image is real.

A student uses a converging lens of focal length $6.0$ cm as a magnifying glass. Starting with the lens very close to a small object, they slowly move the lens away. At first the object appears enlarged and upright, but at a certain point the image suddenly blurs and then reappears upside down.

Explain fully what is happening at each stage, and identify the object distance at which the change occurs.

An object is placed $20$ cm from a converging lens of focal length $8.0$ cm.

Calculate the image distance.

An object $5.0$ cm tall is placed $15$ cm from a converging lens of focal length $10$ cm.

Calculate the image distance and the height of the image, and describe the image fully.

A converging lens has a focal length of $12$ cm. An object is placed first at $18$ cm from the lens, then moved to $8.0$ cm from the lens.

Calculate the image distance and magnification in each case. Explain fully what the change in the sign of the image distance means physically, and explain why the two situations correspond to a projector and a magnifying glass respectively.

State the three properties of the image formed by a diverging lens, for any object position.

An object is placed $20$ cm from a diverging lens of focal length $10$ cm.

Calculate the image distance, and explain why a diverging lens can never form a real image.

A converging lens of focal length $15$ cm and a diverging lens of focal length $15$ cm are each used with an object placed $10$ cm away.

Calculate the image distance and magnification in each case, and compare the two images. Explain fully why the diverging lens behaves the same way for every object distance while the converging lens does not.

State the nature of the image formed by a convex mirror, and give one everyday use of this type of mirror.

An object is placed $12$ cm in front of a concave mirror of focal length $18$ cm.

Calculate the image distance, and describe the image formed. Explain what the sign of your answer tells you.

A car's passenger-side wing mirror is convex with a focal length of $-1.5$ m. A car $2.0$ m tall is $10$ m behind it. The mirror carries the warning "objects in mirror are closer than they appear".

Calculate the image distance and the image height. Explain fully why a convex mirror is used despite this drawback, and explain why the warning is necessary.