Question

What will be the wave velocity, if the radar gives 54 waves per min and the wavelength of the given wave is 10m?
\[
  (a){\text{ 4m}}{{\text{s}}^{ - 1}} \\
  (b){\text{ 6m}}{{\text{s}}^{ - 1}} \\
  (c){\text{ 9m}}{{\text{s}}^{ - 1}} \\
  (d){\text{ 5m}}{{\text{s}}^{ - 1}} \\
\]

Answer 1

Hint: In this question use the direct relation between velocity, frequency and wavelength of a wave that is given by $v = f\lambda $. Direct substitution of values in frequency and wavelength will help getting the value of velocity of the wave.

Complete step-by-step answer:
As we know that the velocity (v) of wave is the product of frequency (f) and wavelength $\left( \lambda \right)$ of the wave.
$ \Rightarrow v = f\lambda $...................... (1)

Where frequency is measured in Hertz (Hz) or in per second and wavelength is measured in meters.

Now it is given that the wavelength of the wave is 10m and the radar gives 54 waves per min.

$ \Rightarrow \lambda = 10m$
And
$ \Rightarrow f = 54$ /min.
Now as we know that in 1 min there is 60 seconds.
$ \Rightarrow f = \dfrac{{54}}{{60}}$ /sec.
Now substitute these values in first equation we have,
$ \Rightarrow v = \dfrac{{54}}{{60}} \times 10 = 9$m/s.
$ \Rightarrow v = 9m{s^{ - 1}}$

So this is the required velocity of the wave.
Hence option (C) is the correct answer.

Additional Information:
Frequency is always inversely proportional to the wavelength so red color has the highest wavelength and is the main reason why it is used in traffic light for stop signal, as it is visible from a very far away distance, however the frequency of red color is the minimum. Blue color is scattered the most, a red wave also travels fastest as velocity is directly dependent upon the wavelength.

Note: Since all the options of this problem were given in $m{s^{ - 1}}$, that’s why the frequency is being converted from unit of wave per minute to wave per second. Frequency itself has the definition of cycles of wave per unit time, so the given information that radar gives 54 waves per min corresponds to frequency.