Answers toStudent Questions

All IB Mathematics IB Sciences IB Individuals & Societies IB Core

Physics

Why does v = fλ?

The universal wave equation v = fλ is one of the fundamental equations in Physics. It relates the speed of a wave, v, the frequency, f, and the wavelength λ. Waves are periodic disturbances that propagate energy through a medium. They are caused by an oscillating source that creates the original disturbance. The frequency of the resulting wave is equal to the frequency of the source. The period $T$ of the oscillation is the inverse of the frequency $f$. One period is the time that it takes for the source to complete a full cycle and return to its original position. The particles in the medium propagate the wave through individual oscillations with this same period. The wavelength $\lambda$ of a wave is defined as the distance between two successive points on a wave that are oscillating in phase. An example of points on a transverse wave that are in phase with each other are crests - at a crest the particles are at the top of their oscillatory motion. Similarly, all points on troughs are in phase with each other. So the distance between adjacent crests or troughs is one wavelength. For a longitudinal wave, a wavelength is the distance between the centers of two adjacent compressions or rarefactions. Now we can think about how far a wave travels in the time that it takes the source disturbance to repeat itself, or in other words, complete one cycle. The time for one cycle is the period $T$. Waves will travel away from the source at a speed $v$. This speed depends on the nature of the medium and is independent of the frequency of the source. If we consider a wave that travels away from the oscillating source, we can use the speed equation $v = \dfrac{s}{t}$ to determine that the distance $s$ that the wave travels in one period $T$ is given by $\hspace{3em} s = vT $ This distance is the separation between two repeating points on the waveform, and so is equal to the wavelength $\lambda$ $\hspace{3em} λ = vT$ Solving for the speed gives $\hspace{3em} v = \dfrac{\lambda}{T}$ And we know that the period is the inverse of the frequency $\hspace{3em}T = \dfrac{1}{f}$ Substituting in, we arrive at the wave equation $\hspace{3em} v = f \lambda$

Chemistry

Why does electronegativity increase across and up the periodic table?

Electronegativity increases across a period (left to right) and up a group because of the combined effects of atomic size and effective nuclear charge. Electronegativity is the ability of an atom to attract the shared pair of electrons in a covalent bond. As you move across a period, the number of protons increases while electrons are being added to the same shell, resulting in a higher effective nuclear charge, which is the net positive charge experienced by valence electrons after accounting for shielding. Since the shielding remains relatively constant across a period (same number of inner shells), the increased nuclear charge pulls the valence electrons more tightly, making the atom smaller and better able to attract bonding electrons. This is why fluorine, at the far right of Period 2, is more electronegative than carbon or nitrogen in the same period. Moving up a group, electronegativity increases primarily due to decreasing atomic size. As you go up a group, there are fewer electron shells between the nucleus and the bonding electrons. For example, fluorine (Period 2) has only two electron shells while iodine (Period 5) has five. When atoms form covalent bonds, the shared electrons in smaller atoms are much closer to the nucleus and experience a stronger electrostatic attraction, despite the smaller number of protons. The effect of decreasing distance outweighs the effect of decreasing nuclear charge as you move up a group. These two trends combine to make fluorine, located in the upper right of the periodic table, the most electronegative element with a value of 4.0, while francium in the lower left would be the least electronegative. The only exception to the trend is the noble gases, which typically don't form bonds and therefore don't have standard electronegativity values.

Environmental Systems and Societies

What is one major cause of species extinction?

Extinctions occur due to changes in a species’ habitat, natural disasters, or direct human actions aimed at the species. Humans are currently driving the **sixth mass extinction** through various factors: - Habitat destruction - Climate change - Introduction of non-native species - Hunting and overharvesting of wild species - Pollution The scale of environmental change and species loss we have caused over the past few centuries has led some scientists to propose naming a new geological epoch: the **Anthropocene**. The **first five mass extinctions** were triggered by natural events such as: - Meteorite impacts - Changes in sea level - Super-volcanic eruptions - Climate change - Tectonic plate movements A key difference between these events and the current mass extinction is the speed. While past extinctions occurred over thousands to millions of years, the current one is unfolding at an accelerated pace due to human activity. It’s important to recognize that extinctions are a natural part of life. As species evolve, they may shift into new niches or change their habitat, leading to the extinction of other species. This, in turn, creates opportunities for new species to evolve and fill the vacated niches. This roughly steady rate of extinction is known as the **background extinction rate**. However, the current extinction rate, driven by human actions, is estimated to be 100 to 10,000 times higher than the natural background rate.

Economics

What are non-price determinants in economics?

Explore More IB Math Resources

Over 80% of IB students globally are experiencing the power of Revision Village

Questionbank

Practice Exams

Key Concepts

Past Papers

Bootcamps & IA Toolkit