4.1.1 Waves transfer energy and information

Waves carry energy without carrying matter

1. A wave begins with an oscillating source, such as a loudspeaker cone, a vibrating string or a dipper in a ripple tank.
2. The source transfers energy to nearby particles or fields, and the disturbance passes from one place to the next.
3. Particles in a material medium oscillate about fixed positions and have no net movement with the wave.
4. A wave can carry information when variations in the wave form a signal, such as speech in sound or digital data in radio waves.

Water waves leave the water behind

1. A floating cork moves up and down as crests and troughs pass, but remains in approximately the same horizontal position.
2. If the water travelled with the wave, the cork would be carried continuously across the tank.
3. The travelling crests and the stationary average position of the cork show that the wave transfers energy without a net transfer of water.

Sound waves leave the air behind

1. A loudspeaker cone moves backwards and forwards, producing compressions and rarefactions in the surrounding air.
2. Each air particle oscillates about a fixed position and transfers energy to neighbouring particles.
3. Sound reaches a listener without producing a continuous wind or moving all the air towards one wall.
4. This shows that the sound disturbance travels while the air has no net movement from speaker to listener.

4.1.2 Frequency, wavelength, amplitude, period and wavefronts

Wave quantities describe size, spacing and timing

1. Frequency has symbol $f$ and unit hertz, $Hz$, where $1Hz$ means one complete oscillation each second.
2. Wavelength has symbol $\lambda$ and SI unit metre, $m$.
3. Measure wavelength from crest to crest, trough to trough or compression to compression.
4. Measure amplitude from the equilibrium line to a crest or trough.
5. The crest-to-trough height is twice the amplitude.

Period is the time for one oscillation

1. Period has symbol $T$ and SI unit second, $s$.
2. Frequency and period are reciprocals: $f=\frac{1}{T}$ and $T=\frac{1}{f}$.

Wavefronts join points moving in step

1. Neighbouring wavefronts are one wavelength apart, and the direction of travel is perpendicular to the wavefronts.
2. A straight source produces plane wavefronts, while a point source produces circular wavefronts.

4.1.3 Longitudinal and transverse waves

Wave type depends on oscillation direction

1. Transverse waves have crests and troughs when shown as displacement diagrams.
2. Electromagnetic waves, seismic S waves and water surface waves are transverse examples.
3. Longitudinal waves contain compressions, where particles are closer together, and rarefactions, where particles are farther apart.
4. Sound waves in air and seismic P waves are longitudinal examples.

Compare oscillation with energy transfer

1. For a transverse wave, the vibration arrow is at $90^{\circ }$ to the direction of travel.
2. For a longitudinal wave, the vibration arrow lies along the direction of travel.
3. Both types transfer energy without a net transfer of matter.

4.1.4 The wave speed equations

Two equations calculate wave speed

1. The frequency-wavelength equation is $v=f\lambda$.
2. The distance-time equation is $v=\frac{x}{t}$.
3. Use $v$ in $m/s$, $f$ in $Hz$, $\lambda$ and $x$ in $m$, and $t$ in $s$.

Rearrange before substituting

1. From $v=f\lambda$, use $f=\frac{v}{\lambda }$ or $\lambda =\frac{v}{f}$.
2. From $v=\frac{x}{t}$, use $x=vt$ or $t=\frac{x}{v}$.
3. Convert units first: $1kHz=10^{3}Hz$, $1MHz=10^{6}Hz$ and $1cm=10^{-2}m$.

Frequency and wavelength vary inversely

1. Wave speed is approximately constant for a wave travelling in a fixed medium.
2. Because $v=f\lambda$, doubling frequency halves wavelength when speed is constant.

4.1.5 Measuring wave velocity

Choose a method that matches the wave

1. A direct method measures distance and time, then uses $v=\frac{x}{t}$.
2. An indirect method measures frequency and wavelength, then uses $v=f\lambda$.
3. Equipment suitability depends on wave speed, available distance and whether wavefronts can be observed or detected.

Measure sound speed electronically

1. Place two microphones a measured distance apart and connect them to an oscilloscope or data logger.
2. Create a short sound near the first microphone and measure the delay between the detected signals.
3. Calculate $v=\frac{x}{t}$ from the separation and delay.
4. A larger separation reduces percentage uncertainty, while electronic timing removes human reaction time.

A boundary changes speed and wavelength

1. When sound enters another medium, frequency stays constant because the source still oscillates at the same rate.
2. Speed changes because wave speed depends on the medium.
3. Since $v=f\lambda$ and $f$ is unchanged, wavelength changes in the same ratio as speed.

4.1.6 Calculating depth or distance from waves

Echo time gives a two-way distance

1. A pulse travels to a boundary, reflects and returns to the detector.
2. The measured echo time is normally the total time for both journeys.
3. The total distance is $x=vt$, so the one-way depth is $d=\frac{vt}{2}$.
4. If the given time is explicitly one-way, do not divide by two.

Use the speed in the stated medium

1. Use the wave speed for the material through which the pulse travels.
2. Typical values are about $340m/s$ in air, $1500m/s$ in water and $3.0\times 10^{8}m/s$ for radio waves in air.
3. Convert times using $1ms=10^{-3}s$ and $1\mu s=10^{-6}s$.

Rearrange for time or speed

1. From $d=\frac{vt}{2}$, use $t=\frac{2d}{v}$ or $v=\frac{2d}{t}$.
2. Keep the factor of two attached to the two-way journey.