Wave speed is the distance a wave travels per unit time.
Quantity: Wave speed (\(v\)) Unit name: metre per
second Unit symbol: \(\text{m·s$^{-1}$}\)
The distance between two successive crests is \(\text{1}\) wavelength, \(λ\). Thus in a time of
\(\text{1}\) period, the wave will travel \(\text{1}\) wavelength in distance. Thus the speed of the
wave, \(v\), is:
However, \(f = \frac{1}{T}\). Therefore, we can also write:
\begin{align*}
v & = \frac{\lambda}{T} \\
& = \lambda \cdot \frac{1}{T} \\
& = \lambda \cdot f
\end{align*}
We call this equation the wave equation. To summarise, we have that \(v = \lambda \cdot f\)
where
\(v =\) speed in \(\text{m·s$^{-1}$}\)
\(\lambda =\) wavelength in \(\text{m}\)
\(f =\) frequency in \(\text{Hz}\)
Wave equation:
\[v = f \cdot \lambda\]
or
\[v = \frac{\lambda}{T}\]
Worked example 4: Speed of a transverse wave I
When a particular string is vibrated at a frequency of \(\text{10}\) \(\text{Hz}\), a
transverse wave of wavelength \(\text{0,25}\) \(\text{m}\) is produced. Determine the
speed of the wave as it travels along the string.
Determine what is given and what is required
frequency of wave: \(f = \text{10}\text{ Hz}\)
wavelength of wave: \(\lambda = \text{0,25}\text{ m}\)
We are required to calculate the speed of the wave as it travels along the string.
The wave travels at \(\text{2,5}\) \(\text{m·s$^{-1}$}\) along the string.
Worked example 5: Speed of a transverse wave II
A cork on the surface of a swimming pool bobs up and down once every second on some ripples.
The ripples have a wavelength of \(\text{20}\) \(\text{cm}\). If the cork is \(\text{2}\)
\(\text{m}\) from the edge of the pool, how long does it take a ripple passing the cork to
reach the edge?
Determine what is given and what is required
We are given:
frequency of wave: \(f = \text{1}\text{ Hz}\)
wavelength of wave: \(\lambda = \text{20}\text{ cm}\)
distance of cork from edge of pool: \(D = \text{2}\text{ m}\)
We are required to determine the time it takes for a ripple to travel between the cork and
the edge of the pool.
The wavelength is not in SI units and should be converted.
Determine how to approach the problem
The time taken for the ripple to reach the edge of the pool is obtained from:
\[t = \frac{D}{v} \qquad \left(\text{from } v = \frac{D}{t}\right)\]
Wave 2: Peak to trough distance (vertical) = \(\text{3}\)
\(\text{cm}\), crest to crest distance (horizontal) = \(\text{5}\)
\(\text{cm}\)
Solution not yet available
You are given the transverse wave below.
Draw the following:
A wave with twice the amplitude of the given wave.
A wave with half the amplitude of the given wave.
A wave travelling at the same speed with twice the frequency of the
given wave.
A wave travelling at the same speed with half the frequency of the
given wave.
A wave with twice the wavelength of the given wave.
A wave with half the wavelength of the given wave.
A wave travelling at the same speed with twice the period of the
given wave.
A wave travelling at the same speed with half the period of the given
wave.
Solution not yet available
A transverse wave travelling at the same speed with an amplitude of \(\text{5}\)
\(\text{cm}\) has a frequency of \(\text{15}\) \(\text{Hz}\). The horizontal
distance from a crest to the nearest trough is measured to be \(\text{2,5}\)
\(\text{cm}\). Find the
period of the wave.
speed of the wave.
Solution not yet available
A fly flaps its wings back and forth 200 times each second. Calculate the period
of a wing flap.
Solution not yet available
As the period of a wave increases, the frequency
increases/decreases/does not change.
Solution not yet available
Calculate the frequency of rotation of the second hand on a clock.
Solution not yet available
Microwave ovens produce radiation with a frequency of \(\text{2 450}\)
\(\text{MHz}\) (\(\text{1}\) \(\text{MHz}\) = \(\text{10}^{\text{6}}\)
\(\text{Hz}\)) and a wavelength of \(\text{0,122}\) \(\text{m}\). What is the
wave speed of the radiation?
Solution not yet available
Study the following diagram and answer the questions:
Identify two sets of points that are in phase.
Identify two sets of points that are out of phase.
Identify any two points that would indicate a wavelength.
Solution not yet available
Tom is fishing from a pier and notices that four wave crests pass by in
\(\text{8}\) \(\text{s}\) and estimates the distance between two successive
crests is \(\text{4}\) \(\text{m}\). The timing starts with the first crest
and ends with the fourth. Calculate the speed of the wave.
