A transverse wave has wavelength of 8.0 meters and frequency 200 Hertz. What is the velocity of the wave?
The correct answer and explanation is :
To find the velocity of a transverse wave, we use the wave speed formula:
$$
\text{Velocity} = \text{Wavelength} \times \text{Frequency}
$$
Given:
- Wavelength ($\lambda$) = 8.0 meters
- Frequency ($f$) = 200 Hertz
$$
v = \lambda \cdot f = 8.0 \, \text{m} \times 200 \, \text{Hz} = \boxed{1600 \, \text{m/s}}
$$
Explanation (300 words):
Waves are a method of energy transfer, and they can be classified in various ways. A transverse wave is a type of mechanical wave where the particles of the medium move perpendicular to the direction the wave travels. Examples of transverse waves include light waves and water waves.
In wave mechanics, three core properties are usually considered: wavelength, frequency, and velocity (or speed). The wavelength is the distance between two successive crests (or troughs) of a wave and is measured in meters. The frequency is the number of wave cycles that pass a fixed point per second and is measured in Hertz (Hz). The velocity (or speed) is how fast the wave propagates through the medium.
These three are connected through the formula:
$$
v = \lambda \cdot f
$$
This formula shows that the speed of a wave is equal to the product of its wavelength and frequency. It applies to all types of waves, including sound waves, light waves, and water waves, as long as the wave travels through a medium or space consistently.
In this specific problem, the wavelength is 8.0 meters, meaning the distance between repeating points in the wave is 8 meters. The frequency is 200 Hz, meaning 200 waves pass a given point every second. By multiplying the two values, we find that the wave covers 1600 meters every second, or 1600 m/s.
Understanding wave velocity is important in physics and engineering, as it helps in analyzing signals, sound, and even seismic activity. It also illustrates the interdependence of physical properties in dynamic systems.