Gravitational waves travel at the speed of light. Their speed, wavelength, and frequency are related as \(c=\lambda \times f\). If we were to observe a gravitational wave from a distant cosmic event with a frequency of 10 hertz \((\mathrm{Hz}),\) what would be the wavelength of the gravitational wave?

Gravitational waves travel at the speed of light, which is a fundamental constant in physics. The speed of light, denoted as \(c\), is approximately \(3 \times 10^8 \text{ m/s}\). This is the maximum speed at which all energy, matter, and information in the universe can travel.
To understand gravitational waves, it's essential to recognize that they share this remarkable speed with light waves. This speed is crucial when calculating properties such as wavelength and frequency for any wave traveling at light speed.
In the exercise, we calculate the wavelength of a gravitational wave using its speed and frequency, leveraging this fundamental constant.

The wavelength of a wave represents the distance between successive peaks (or troughs) of the wave. For gravitational waves, the wavelength is related to the speed of light and the frequency of the wave by the equation \(c = \lambda \times f\).
The wavelength \(\lambda\) can be found by rearranging the formula to\[\lambda = \frac{c}{f}\]
In the given exercise, to find the wavelength of a gravitational wave with a frequency of 10 Hz, we use the formula with known values for the speed of light and frequency:

\t
• Speed of light, \(c = 3 \times 10^8 \text{ m/s}\)
\t
• Frequency, \(f = 10 \text{ Hz}\)

By substituting these values, we get the wavelength as \(3 \times 10^7 \text{ m}\).

Frequency, denoted by \(f\), is the number of wave cycles that pass a point per second. It is measured in Hertz (Hz). Higher frequencies mean more cycles per second, while lower frequencies mean fewer cycles per second.
In the context of gravitational waves, the frequency determines how often the waves oscillate per second. In the exercise, we consider a gravitational wave with a frequency of 10 Hz. This means the wave oscillates 10 times each second.
Understanding frequency is essential for calculating other properties of waves, such as their wavelength when combined with the speed of light. Remember, high frequency waves will have shorter wavelengths and vice versa.

Gravitational waves originate from massive cosmic events, such as the collision of black holes or neutron stars. These events are so powerful that they create ripples in the fabric of spacetime, which travel outwards at the speed of light.
Detecting and analyzing these waves gives scientists essential insights into these distant occurrences. By measuring the frequency and wavelength of gravitational waves, researchers can determine the nature and distance of the events that created them.
In the exercise, we observe a gravitational wave from a distant cosmic event with a frequency of 10 Hz. This calculation helps us understand more about the origins and properties of the truly massive and dynamic phenomena occurring far out in the universe.