Question

Calculate the wavelength of a wave if it travels with speed $2\,cm/s$ and period is $2\,s$.
A) $0.25 cm$
B) $0.5 cm$
C) $1 cm$
D) $2 cm$
E) $4 cm$

Answer 1

The wavelength of a wave is the distance between two crests or two troughs. The wavelength is related to the velocity of the wave and its frequency.

Formula used: In this solution, we will use the following formula:
The velocity of a wave: $v = f\lambda$ where, $f$ is the frequency of the wave and $\lambda$ is the wavelength

Complete step by step answer:
We’ve been given that the wave travels with speed $2cm/s$ and period is $2s$. The wavelength of a wave is related to its velocity and its frequency as
$v = f\lambda$
Speed of the wave is $2cm/s$ hence $v = 2cm/s$
The frequency of the wave is the inverse of the time period of the wave. So if the time period of the wave is $2s$, its frequency will be
$f = \dfrac{1}{T} = \dfrac{1}{2}$
Which gives us
$f = 0.5{s^{ - 1}}$
Using these values in the formula $v = f\lambda$, we get
$2 = 0.5\lambda$
Dividing both sides by $0.5$, we get
$\lambda = 4cm$
Hence the wavelength of the wave travelling with a speed $2cm/s$ and having a time period of $2s$ is $\lambda = 4cm$ which corresponds to option (E).

Note: The frequency is the inverse of the time period as the frequency of the wave can be thought of as the number of times a wave travels through a certain point in one second. This can then help us to break down the relation of the wavelength of a wave as:
$v = \dfrac{\lambda }{T}$
If we think of $\lambda$ as the distance traveled by the wave, the speed of the wave can be thought of as the distance traveled by the wave in one time period. This relation is very similar to the relation of speed with distance and time of any object where
${\text{speed = }}\dfrac{{{\text{distance}}}}{{{\text{time}}}}$