Waves, Light and Sound

The frequency of a wave is the number of complete waves (oscillations) passing a fixed point per second. It is measured in hertz ($\text{Hz}$), where $1\,\text{Hz}$ means one complete wave per second.

Step 1 — State the formula:

$$ T = \frac{1}{f} $$

Step 2 — Substitute:

$$ T = \frac{1}{50} $$

Answer: $T = 0.02\,\text{s}$

Step 1 — Rearrange $v=f\lambda$ for $f$:

$$ f = \frac{v}{\lambda} $$

Step 2 — Substitute:

$$ f = \frac{340}{0.68} $$

Answer: $f = 500\,\text{Hz}$

In a transverse wave, the particles (or field) vibrate at right angles (perpendicular) to the direction the wave travels — for example, a light wave or a wave on a shaken rope.

In a longitudinal wave, the particles vibrate parallel to (along the same line as) the direction the wave travels, creating compressions and rarefactions — for example, a sound wave.

Benefit: Because tsunami wave speed can be calculated fairly reliably from ocean depth data, scientists can predict, often with tens of minutes to hours of warning, when a wave will reach a populated coastline. This gives coastal communities time to evacuate to higher ground, potentially saving thousands of lives compared to having no warning system.

Drawback: The calculation depends on accurate, detailed data about ocean depth along the wave's whole path, and on correctly detecting the earthquake itself — if this data is incomplete or the earthquake is very close to shore, there may not be enough warning time, or the predicted arrival time could be wrong. False alarms can also occur, which may lead communities to distrust or ignore future warnings ("warning fatigue").

Benefit: Even a warning of just a few seconds is enough for people to take protective action — dropping, covering, and holding on, stepping away from windows, or for automatic systems to stop trains, open elevator doors, or pause surgery, significantly reducing injuries and damage from the more destructive S-waves and the shaking that follows.

Drawback: The warning time is often very short (seconds, not minutes) and depends on how far away the earthquake's origin is, so it may be too brief to be useful for earthquakes that start very close to a city. Access to the technology is also unequal — it relies on a dense network of sensors and on people owning smartphones with the app installed, meaning wealthier regions typically benefit far more than poorer ones, even though the risk from earthquakes is not limited to wealthy areas.

Benefit: Radio waves allow instant wireless communication over large distances without needing physical cables, enabling mobile phones, GPS navigation, emergency service coordination, and internet access almost anywhere. This has transformed how people work, travel, and respond to emergencies, and has made information and connectivity available to people in remote areas that cables would be impractical to reach.

Concern: Because so many different services (phones, WiFi routers, radio, television, satellites) all need their own slice of the same limited radio spectrum, overcrowding and interference between signals is an ongoing challenge, requiring careful regulation of which frequencies each service is allowed to use. There has also been public concern about possible long-term health effects of continuous exposure to radio-frequency waves from phones and masts — although major scientific reviews have found no confirmed harm at the low power levels used, the concern has still shaped where phone masts can be built and how devices are designed and tested.

Sound is a longitudinal mechanical wave — it travels by making particles of a medium (like air, water, or a solid) vibrate and pass the vibration on to neighbouring particles. In a vacuum there are no particles to vibrate, so sound cannot be transmitted. Light, on the other hand, does not need a medium to travel — it is an electromagnetic wave and can travel through empty space, which is why we can see distant stars and the Sun's light reaches us through the vacuum of space.

Step 1 — Note that the sound travels to the cliff AND back, so halve the total distance:

$$ \text{total distance} = v \times t = 340 \times 1.2 = 408\,\text{m} $$

Step 2 — Divide by 2 for the one-way distance:

$$ \text{distance to cliff} = \frac{408}{2} $$

Answer: $204\,\text{m}$

Step 1 — Find the total distance travelled by the pulse (down AND back up):

$$ \text{total distance} = 2 \times 1500 = 3000\,\text{m} $$

Step 2 — Apply $v = \dfrac{\text{distance}}{\text{time}}$:

$$ v = \frac{3000}{2.0} $$

Answer: $v = 1500\,\text{m/s}$

Benefit: Unlike X-rays, ultrasound does not use ionising radiation, so it is considered very safe to use repeatedly, including on unborn babies and pregnant patients, with no known harmful side effects at the intensities used. It also produces images in real time, allowing doctors to see movement, such as a beating heart, immediately.

Drawback: Ultrasound images generally have lower resolution and detail than other scanning methods such as MRI, and the quality of the image depends heavily on the skill of the person operating the probe. Ultrasound also struggles to pass through bone or air-filled spaces (like the lungs), so it is not suitable for imaging every part of the body.

Benefit: Headphones allow people to enjoy music, podcasts, and calls privately and conveniently, anywhere, without disturbing others — supporting entertainment, relaxation, focus while working or studying, and accessible communication, all without needing external speakers.

Drawback: Many people listen at volumes close to or above $100\,\text{dB}$, well above the $85\,\text{dB}$ threshold linked to hearing damage, often for long periods. Repeated exposure at these levels can cause permanent, irreversible hearing loss or tinnitus (persistent ringing in the ears), especially among younger people who may not realise the damage is accumulating until symptoms appear later in life.

Benefit: Sonar allows ships to accurately map the seabed and detect obstacles, greatly improving navigational safety, and allows fishing fleets to locate fish stocks efficiently, and navies and rescue teams to detect submarines or sunken vessels — all without needing to see through the water, which is usually impossible at depth.

Concern: Many marine mammals, such as whales and dolphins, rely on their own natural echolocation (a biological form of sonar) to navigate, communicate, and find food. Loud, high-powered sonar used by ships and navies can interfere with this, disorient the animals, or even cause physical harm to their hearing, and has been linked by some researchers to mass whale strandings. This has led to calls for stricter regulation of sonar use, particularly in areas known to be important marine mammal habitats.

The image formed by a plane mirror is:

1. Virtual — it cannot be projected onto a screen, since the light rays only appear to come from behind the mirror.
2. The same size as the object.
3. Laterally inverted — left and right are swapped (e.g. text appears back-to-front).
4. The same distance behind the mirror as the object is in front of it.

Benefit: Optical fibres can carry enormous amounts of data at extremely high speed over very long distances with very little signal loss, and are not affected by electrical or magnetic interference the way old copper cables are — this has made fast, reliable global internet and communication possible on a scale that older technologies could not support.

Drawback: Installing optical fibre networks is expensive and disruptive, requiring cables to be laid underground or undersea across huge distances, and the thin glass fibres are relatively fragile and can be damaged (e.g. by construction work), requiring specialist equipment and expertise to repair. This means fibre access has been rolled out unevenly, with rural and lower-income areas often gaining access much later than wealthier or denser urban areas.

Benefit: Endoscopes allow doctors to examine or operate inside the body through a very small opening, which is far less invasive than traditional open surgery — this generally means less pain, a lower risk of infection, and a much faster recovery time for the patient.

Drawback: Endoscopic equipment is expensive and requires specially trained staff to operate safely and interpret the images correctly, meaning it is not equally available in all hospitals worldwide, particularly in poorer regions. There is also still some risk of discomfort, injury, or infection associated with inserting the endoscope, even though this risk is lower than with open surgery.

Benefit: Concentrated solar power generates electricity from sunlight, a renewable resource, without producing the greenhouse gas emissions associated with burning fossil fuels. Unlike some other forms of solar power, the heat it captures can be stored and used to generate electricity even after the Sun has set, helping to provide a more continuous, reliable supply of clean energy.

Concern: These plants require very large areas of land for the mirror arrays, which is often desert habitat that can still be home to wildlife — the intense concentrated light and heat around the central tower has also been reported to injure or kill birds and insects that fly through the focused beam. Building and maintaining such large reflective installations is also costly, and finding suitable large, sunny, flat sites is not possible everywhere.

All electromagnetic waves travel through a vacuum at the same speed, $c = 3\times10^{8}\,\text{m/s}$ (the speed of light). This is unusual because it applies to every type of electromagnetic wave — radio waves, infrared, visible light, X-rays, and so on — despite them having enormously different wavelengths and frequencies; unlike sound, their speed in a vacuum does not depend on wavelength or frequency at all.

Step 1 — Rearrange for $f$:

$$ f = \frac{c}{\lambda} $$

Step 2 — Substitute:

$$ f = \frac{3\times10^{8}}{3} $$

Answer: $f = 1\times10^{8}\,\text{Hz} = 100\,\text{MHz}$, a typical FM radio frequency.

Step 1 — Rearrange $c=f\lambda$ for $\lambda$:

$$ \lambda = \frac{c}{f} $$

Step 2 — Substitute:

$$ \lambda = \frac{3\times10^{8}}{3\times10^{18}} $$

Answer: $\lambda = 1\times10^{-10}\,\text{m}$, a typical X-ray wavelength.

Across the electromagnetic spectrum, shorter wavelength corresponds to higher frequency, and higher frequency electromagnetic waves carry more energy. UV radiation has a very short wavelength and therefore a very high frequency, compared to radio waves, which have an extremely long wavelength and very low frequency. This is why UV radiation carries enough energy to damage skin cells and cause sunburn, while radio waves (used for broadcasting and communication) are considered low-energy and harmless at everyday exposure levels.

Benefit: X-ray imaging is quick, relatively low-cost, and gives doctors detailed images of bones and some internal structures almost immediately, without needing invasive surgery — this allows fractures, some tumours, and other internal problems to be diagnosed and treated rapidly, which can be critical in emergencies.

Drawback: Because X-rays are ionising radiation, they can damage living cells and increase the risk of cancer with repeated exposure over a lifetime. For this reason, hospitals strictly limit how many X-rays a patient receives, use lead aprons and shielding to protect other parts of the body and staff, and avoid X-rays for pregnant patients where possible, using safer imaging methods (such as ultrasound) instead when appropriate.

Benefit: Wireless communication gives people near-constant access to information, education, work, and emergency services, wherever they are, without needing physical cables — this has transformed education, business, and personal safety (for example, being able to call for help from almost anywhere).

Concern: With so many devices using the same limited ranges of frequencies, signal congestion and interference between networks is an ongoing challenge that requires careful regulation of which frequencies each type of device is allowed to use. There has also been public concern about possible long-term health effects of continuous exposure to radio-frequency radiation from phones and masts; although major scientific reviews have found no confirmed harm at the low power levels used, ongoing monitoring and research is still considered important as usage continues to grow.

Benefit: Gamma radiation can sterilise medical equipment (such as syringes and surgical instruments) thoroughly without using heat, which is essential for equipment that would be damaged by traditional heat sterilisation, helping prevent the spread of infection. In radiotherapy, carefully targeted and controlled doses of gamma radiation can destroy cancerous tumour cells, and has become one of the most important treatments for saving the lives of cancer patients worldwide.

Drawback: Gamma radiation is highly ionising and dangerous — it can damage or kill healthy living cells just as it can kill bacteria or cancer cells, so equipment producing or using it requires thick shielding (often lead or concrete) and strict safety procedures for the staff who work with it. In radiotherapy specifically, some healthy tissue surrounding a tumour is inevitably exposed too, causing side effects such as fatigue, skin irritation, or damage to nearby healthy organs, meaning doctors must carefully balance the dose needed to treat the cancer against the harm caused to the patient's healthy cells. Safe long-term disposal of radioactive sources used in this equipment is also a significant ongoing challenge.