Question

Calculate the period of a wave which is having wavelength $17m$ and wave velocity $340m/s$.

Answer 1

This problem can be solved by the direct formula for the speed of a wave in terms of its wavelength and its time period. The wavelength is the distance travelled by the wave in one time period and speed is the ratio of distance to time.

Formula used:
$v=\dfrac{\lambda }{T}$

Complete step by step answer:
The wavelength of a wave is the distance travelled by the wave in one time period. Since, speed is defined as the ratio of the distance travelled to the time interval, it can be derived that the speed of the wave is the ratio of the distance travelled in one time period to the time period. Hence, the speed of the wave is the ratio of the wavelength to the time period of the wave.
Therefore, the speed $v$, wavelength $\lambda$ and time period $T$ of a wave are related as
$v=\dfrac{\lambda }{T}$ --(1)
Now, let us analyze the question.
The speed of the wave is given to be $v=340m/s$.
The wavelength of the wave is given to be $\lambda =17m$.
Let the time period of the wave be $T$.
Therefore, using (1), we get
$v=\dfrac{\lambda }{T}$
$\therefore T=\dfrac{\lambda }{v}$
$\therefore T=\dfrac{17}{340}=\dfrac{1}{20}=0.05s$
Hence, the required time period of the wave is $0.05s$.

Note: Students must note that the speed of a wave is defined for a specific medium. If the wave passes from one medium to another, then the speed changes. This is because the wavelength of the wave changes and by equation (1), the speed is bound to change as the time period of the wave does not change. Similarly, the frequency (inverse of the time period) of the wave also does not change when going from one medium to another.