Question 1: Define the wave equation relating wave speed, wavelength, and frequency.

Answer: Wave speed (v) equals wavelength (λ) times frequency (f), expressed as v = λ × f.

Question 2: Explain why the wave speed remains constant in a given medium, regardless of the frequency or wavelength.

Answer: In a constant medium, the wave speed is determined by the properties of the medium and does not change with frequency or wavelength.

Question 1: A wave has a wavelength of 0.5 meters and a frequency of 10 Hz. Calculate its wave speed in meters per second.

Answer: Wave speed v = λ × f = 0.5 m × 10 Hz = 5 m/s

Question 2: A wave traveling in water has a speed of 1500 m/s and a wavelength of 3 meters. What is its frequency?

Answer: f = v / λ = 1500 m/s / 3 m = 500 Hz

Question 1: Describe a simple experiment to demonstrate how wave speed depends on the medium.

Answer: One experiment involves transmitting a pulse along different materials (e.g., string, water, metal) and measuring the time it takes for the pulse to travel a fixed distance; wave speed varies depending on the medium's properties.

Question 2: Identify safety precautions students should take when conducting wave experiments involving electrical equipment or vibrations.

Answer: Ensure equipment is properly grounded, avoid contact with moving parts, and handle electrical devices with dry hands to prevent shocks.

Question 1: A scientist measures the wavelength of a certain wave as 2 meters and finds its speed to be 600 m/s. What is the frequency of the wave?

Answer: f = v / λ = 600 m/s / 2 m = 300 Hz

Question 2: In a certain medium, waves with a frequency of 50 Hz have a wavelength of 4 meters. What is the wave speed?

Answer: v = λ × f = 4 m × 50 Hz = 200 m/s

Question 1: Explain how the wave equation v = λ × f applies to the design of communication systems such as radio and television signals.

Answer: The wave equation relates wave speed, wavelength, and frequency, which are critical in designing signals for communication systems. Adjusting frequency and wavelength allows signals to travel efficiently over long distances without interference, enabling effective transmission of radio and TV broadcasts.

Question 2: A wave has a speed of 300 m/s and a wavelength of 0.75 meters. What is its frequency? Show your work.

Answer: f = v / λ = 300 m/s / 0.75 m = 400 Hz

Question 1: Describe how understanding wave equations helps in designing ultrasound medical imaging devices.

Answer: Wave equations help determine the frequency and wavelength of ultrasound waves, ensuring they penetrate tissues effectively and produce clear images for diagnosis.

Question 2: Explain the importance of wave speed calculations in the telecommunications industry, especially for fiber optic cables.

Answer: Accurate wave speed calculations ensure signals are transmitted efficiently over long distances without distortion, enabling high-speed internet and reliable communication.