Question

How can you calculate the wavelength from speed?

Answer 1

Hint: In this question, we will directly use the basic relation between speed, frequency and the wavelength of a given wave or radiation. Further, we will study the basic difference between speed and velocity. We will also study the basic definition of frequency, for our better understanding.

Formula used:
$f = \dfrac{c}{\lambda }$

Complete solution:
As we know, there is a relation between the wavelength, speed of light c and frequency f. this relation is given by:
$f = \dfrac{c}{\lambda }$
We know the speed of light c is equal to $3 \times {10^8}m/s$.

Now, the above equation can also be written as:
$f = \dfrac{v}{\lambda }$
$\therefore \lambda = \dfrac{v}{f}$

Therefore, we get the required expression to calculate wavelength with speed v.

Additional information:
We already know the basic difference of speed and velocity i.e., speed is the measure of how fast an object can travel, whereas velocity tells us the direction of this speed. Here, speed is a scalar quantity that means that speed has only magnitude, whereas velocity is a vector quantity that means velocity has both magnitude as well as direction. Now, the S.I unit of velocity is meter per second which is represented by m/sec.

Also, we know that the speed of sound is different in different mediums. Further, we know that the speed is more than the speed of sound is termed differently like- supersonic, hypersonic etc

Further, we know that the frequency can be defined as the number of waves that pass a fixed point in a unit time. Also, the S.I unit of frequency is Hertz or it is represented by Hz and the unit of wavelength is meter or it is represented by m.

Note:
This question can be directly answered by knowing the basic relation between speed and wavelength. Also, we know speed does not have any direction unlike velocity therefore, we can say that speed cannot be negative. We must remember that the unit of speed and velocity is the same i.e., meter per sec or m/s.