Physics: TestAS practice testlets

A wave transports energy without transporting matter. In a transverse wave, such as a wave on a rope or a light wave, the oscillation is perpendicular to the direction of travel; in a longitudinal wave, such as sound in air, it is parallel. Every wave is characterised by its wavelength λ, the distance between two neighbouring crests, its frequency f, the number of oscillations per second in hertz, and its speed v. The three are linked by v = f·λ. The amplitude, the maximum displacement, determines the energy carried: for sound, it corresponds to loudness; the frequency corresponds to pitch.

v = f·λ c ≈ 3 × 10⁸ m/s (light) v_sound ≈ 340 m/s (air)

Sound needs a medium and cannot travel through a vacuum. In air, it travels at about 340 m/s; in water, about four times faster. Humans hear frequencies from about 20 Hz to 20 kHz. Light is an electromagnetic wave and needs no medium; in a vacuum, it travels at about 3 × 10⁸ m/s. Visible light, with wavelengths from about 400 nm (violet) to 700 nm (red), is only a small part of the electromagnetic spectrum. In order of increasing frequency, and decreasing wavelength, the spectrum comprises radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Higher frequency means more energy per photon, which is why ultraviolet light, X-rays and gamma rays can damage living cells.

When waves meet, they superpose. If crests meet crests, they reinforce each other (constructive interference); if crests meet troughs, they cancel (destructive interference). Noise-cancelling headphones use destructive interference. When a wave passes from one medium into another, its speed changes and it may change direction, a process called refraction; its frequency stays the same, so its wavelength changes. Refraction makes a straw in a glass of water appear bent and allows lenses to focus light.

The Doppler effect is the change in observed frequency when the source and the observer move relative to each other: the pitch of an ambulance siren is higher as it approaches and lower as it moves away. Astronomers use the same effect to measure how fast galaxies move away from us.

When an object is thrown or launched and then moves only under the influence of gravity, its path is called a trajectory. If air resistance is neglected, the motion can be analysed by splitting it into two independent parts. Horizontally, no force acts, so the horizontal velocity stays constant. Vertically, gravity causes a constant downward acceleration g of about 9.81 m/s², which we round to 10 m/s² here. Combining a constant horizontal velocity with a uniformly accelerated vertical motion produces a parabolic path.

horizontal: x = v_x·t vertical (from rest): y = ½·g·t² g ≈ 10 m/s²

A classic consequence concerns two balls released from the same height at the same moment, one dropped and one thrown horizontally. Because their vertical motions are identical, both hit the ground at the same time; the thrown ball simply travels further horizontally. The time of flight depends only on the height of the fall, not on the horizontal speed.

For an object launched at an angle from level ground, its initial velocity is split into a horizontal component and a vertical component. The vertical component determines how high it rises and how long it stays in the air; the horizontal component determines how far it travels in that time. Ignoring air resistance, the range is greatest for a launch angle of 45°, and complementary angles such as 30° and 60° give equal ranges. In reality, air resistance reduces both height and range and makes the path asymmetric; for a ball in sport, the best angle is usually somewhat lower than 45°.

At the highest point of the path, the vertical velocity is momentarily zero, but the horizontal velocity is unchanged, so the object is still moving. The acceleration is g downwards at every point of the path, including the top.

Engineers and athletes use these ideas in practice. The design of fountains, the aiming of water jets in firefighting and the analysis of long jumps and shot puts all rely on splitting motion into horizontal and vertical components. For objects moving fast or far, such as artillery shells or golf balls, air resistance and spin must be included, which requires numerical calculations.

A stone is thrown horizontally from the edge of a cliff 20 m above the sea, with a speed of 15 m/s. Air resistance is neglected.