Answer to Question #207887 in Molecular Physics | Thermodynamics for Ankush

Question

A transmitted wave with a length of 2.00 m can travel 75.0 m in 30.0 s. If  the wave was travelling at 3.00 m/s in the initial medium, what was the  wavelength? 

Answer 1

 We know velocity is directly proportional to the wavelength of the wave.

i.e $λ ∝ V$

So, $λ1/λ2 = V1/V2$

Wavelength, $λ2 = 2$ m

Traveled distance $= 75$ m

Time used to travell $= 30$ s

So, Velocity of the wave at the beginning

V2= (

Traveled distance/Time used).

$= (75/30)$ m/s

 $= 2.5$ m/s

    

Velocity of the wave in initial medium, $V1 = 3$ m/s

Let,

initial wavelength was $= λ1$ m

We know,.  $λ1/λ2 = V1/V2$

         Or, $λ1 = (V1/V2)×λ2$

                $= (3/2.5)×2$ m

           $= 2.4$ m

In the initial medium, the wavelength $= 2.4$ m