Aperiodic wave can be mathematically written as = − 1. what part of the wave does a describe? 2. if we take a snapshot of the wave, what is the distance between two crests (or troughs) called? how is this related to k? 3. the source that is generating the wave oscillates with a frequency of f . how is this related to 4. write down the relationship between wave speed, wave frequency and wavelength.

A periodic wave can be written as:

where

A is the amplitude, k is the wave number, x is the position, is the angular frequency and t is the time.

1. A represents the amplitude

Explanation: the term A inside the wave equation represents the amplitude, which is the maximum displacement of the wave (along the y-axis) with respect to tis equilibrium position. Basically, when the sine part of the wave is equal to 1, y=A, and the wave has the maximum displacement.

2. Wavelength

Explanation: the wavelength of a wave is defined as the distance between two successive crests (or between succesive throughs) of the wave.

The wavelength (indicated with ) is related to the wave number, k, by the equation

3.

The frequency at which the source of the wave is oscillating, f, is related to the angular frequency by the relationship

basically, f expresses the frequency in units of Hertz (1/s), while the angular frequency expresses the frequency in units of radians per second.

4.

The relationship between wave speed, wave frequency and wavelength is

where

v is the wave speed

f is the frequency

is the wavelength

We can observed that if the speed of the wave is constant, then the frequency and the wavelength are inversely proportional to each other.