Speed of a longitudinal wave
The speed of a longitudinal wave is defined in the same was as the speed of transverse waves:
 Definition 1: Wave speed
Wave speed is the distance a wave travels per unit time.
Quantity: Wave speed (v) Unit name: speed Unit: m·s^{−1}
The distance between two successive compressions is 1 wavelength, λ. Thus in a time of 1 period, the wave will travel 1 wavelength in distance. Thus the speed of the wave, v, is:
However, $f=\frac{1}{T}$. Therefore, we can also write:
We call this equation the wave equation. To summarise, we have that $v=\lambda \xb7f$ where

$v=$ speed in m·s^{−1}

$\lambda =$ wavelength in m

$f=$ frequency in Hz
Example 1: Speed of longitudinal waves
Question
The musical note “A” is a sound wave. The note has a frequency of 440 Hz and a wavelength of 0,784 m. Calculate the speed of the musical note.
Answer
Determine what is given and what is required
Using:
We need to calculate the speed of the musical note “A”.
Determine how to approach based on what is given
We are given the frequency and wavelength of the note. We can therefore use:
Calculate the wave speed
Write the final answer
The musical note “A” travels at 345 m·s^{−1}.
Example 2: Speed of longitudinal waves
Question
A longitudinal wave travels into a medium in which its speed increases. How does this affect its... (write only increases, decreases, stays the same).

period?

wavelength?
Answer
Determine what is required
We need to determine how the period and wavelength of a longitudinal wave change when its speed increases.
Determine how to approach based on what is given
We need to find the link between period, wavelength and wave speed.
Discuss how the period changes
We know that the frequency of a longitudinal wave is dependent on the frequency of the vibrations that lead to the creation of the longitudinal wave. Therefore, the frequency is always unchanged, irrespective of any changes in speed. Since the period is the inverse of the frequency, the period remains the same.
Discuss how the wavelength changes
The frequency remains unchanged. According to the wave equation
if f remains the same and v increases, then λ, the wavelength, must also increase.