Question 1: Define the wave equation relating wave speed (v), frequency (f), and wavelength (λ).

Answer: The wave equation is v = f × λ, where v is the wave speed, f is the frequency, and λ is the wavelength.

Question 2: Explain what is meant by the term 'wave speed' in the context of wave properties.

Answer: Wave speed is the distance a wave travels per unit time, typically measured in metres per second (m/s).

Question 3: Which of the following correctly represents the relationship between wavelength, frequency, and wave speed?

Answer: v = λ × f

Question 4: Fill in the blank: The wavelength of a wave is inversely proportional to its __________ when wave speed is constant.

Answer: frequency

Question 5: Describe how the wavelength of a wave changes if the wave speed remains constant but the frequency increases.

Answer: If the wave speed remains constant and the frequency increases, the wavelength decreases.

Question 6: Calculate the wavelength of a wave that has a speed of 300 m/s and a frequency of 50 Hz.

Answer: λ = v / f = 300 / 50 = 6 metres

Question 7: A wave has a wavelength of 2 metres and a frequency of 150 Hz. What is its speed in m/s?

Answer: v = f × λ = 150 × 2 = 300 m/s

Question 8: Identify three variables that affect the speed of a wave in a medium.

Answer: The properties of the medium (such as density and elasticity), the type of wave, and temperature can affect wave speed.

Question 9: Explain why electromagnetic waves do not require a medium to travel and how their speed relates to the wave equation.

Answer: Electromagnetic waves do not require a medium because they are oscillations of electric and magnetic fields that propagate through space. Their speed in a vacuum, approximately 3 × 10^8 m/s, is a constant and can be described by the wave equation v = f × λ, where both frequency and wavelength are related to the properties of the electromagnetic wave, but the medium is not a factor.

Question 10: In practical applications, how is the wave equation used in the design of communication systems such as radio or microwave transmission?

Answer: The wave equation helps engineers determine the appropriate wavelength and frequency for effective transmission, ensuring signals travel efficiently over distances without interference, and allows for the calculation of necessary antenna sizes based on wavelength.