A tuning fork produces longitudinal waves, as the vibrations cause compressions and rarefactions in the air.

A vibrating tuning fork produces longitudinal waves in the air, which then can create transverse waves in the surface of the table.

Sound is classified as a longitudinal wave, where the particle displacement is parallel to the direction of wave propagation.

Setting 2(1) + 1 = a and a = 2 for continuity.

Setting 2(3) + a = 5 gives a = -1.

Setting 4 = 2 gives a = 1 for continuity.

Setting the left limit (k(1) = k) equal to the right limit (1 + 1 = 2), we find k = 2.

Setting the left limit (3(2) + 1 = 7) equal to the right limit (2^2 - 1 = 3), we find m = 3.

The reaction is Na2CO3 + 2 HCl → 2 NaCl + H2O + CO2. 0.1 moles of Na2CO3 requires 0.2 moles of HCl. Volume = moles / concentration = 0.2 moles / 0.5 M = 0.4 L or 400 mL.

Using the formula Molarity (M) = moles/volume (L), we have 0.5 M = 1 mole/volume. Therefore, volume = 1 mole / 0.5 M = 2 L.

Using the formula Molarity (M) = moles/volume (L), we rearrange to find volume = moles/Molarity. Thus, volume = 1 mole / 0.5 M = 2 L.

The reaction between NaOH and HCl is 1:1. Therefore, to neutralize 0.5 moles of HCl, 0.5 moles of NaOH are required, which corresponds to 0.5 L of 1 M NaOH solution.

The population explosion led to increased migration to colonies as people sought new opportunities and resources.

The steam engine was a major technological advancement that powered factories and revolutionized transportation during the Industrial Revolution.

Deforestation was a significant environmental consequence of the Industrial Revolution, as forests were cleared for factories, urban development, and agriculture, leading to habitat loss.

The Tangshan earthquake prompted China to introduce stricter building codes to mitigate the impact of future earthquakes.

Urbanization and overcrowding were negative consequences of the Industrial Revolution, as people moved to cities for factory jobs.

The Industrial Revolution was significantly driven by Britain's abundant natural resources, particularly coal and iron, which were essential for powering machinery and building infrastructure.

The average monthly sales in 2020 was 1500 as shown in the line chart.

Pataliputra was the capital of the Maurya Empire and served as a major political and cultural center during Ashoka's reign.

Pataliputra, located near modern-day Patna, served as the capital of the Maurya Empire.

Pataliputra, located near modern-day Patna, served as the capital of the Maurya Empire.

India's GDP growth rate in the first quarter of 2023 was reported at 6.1%.

India's GDP growth rate for the fiscal year 2022-2023 was approximately 7.2%.

The Black Death led to the establishment of quarantine measures as a public health response to control the spread of the plague.

The Columbian Exchange had a profound impact on global agriculture by introducing new crops, increasing biodiversity, and also spreading diseases.

The Industrial Revolution increased child labor, as factories employed children for low wages and long hours.

The launch of the Hubble Space Telescope in 1990 significantly enhanced our understanding of the universe by providing clearer images of celestial bodies, leading to numerous discoveries in astronomy.

The fall of the Western Roman Empire was due to a combination of economic troubles, barbarian invasions, and political corruption.

The French Revolution was primarily caused by an economic crisis, widespread discontent with high taxes, and the influence of Enlightenment ideas advocating for liberty and equality.