Question

A wave of a time period of $20ms$ travel with a velocity of $2m{s}^{-1}$If the time period of another wave is$5ms$, then the velocity of the second wave and the ratio of their velocity is

(wave length of the two waves is same) _______ and _______, respectively

• A. $0.8m{s}^{-1},\frac{7}{2}$
• B. $0.25m{s}^{-1},\frac{5}{2}$
• C. $8m{s}^{-1},\frac{1}{4}$
• D. $Noneofthese$

Answer 1

The correct option is C

$8m{s}^{-1},\frac{1}{4}$

Let,

The time period of the first wave is $T_1$

The time period of the second wave$T_2$

The velocity of the first wave is $v_1$

The velocity of the second wave is$v_2$

STEP 1: GIVEN DATA

Given,

$T_1=20ms$ $v_1=2m{s}^{-1}$

$T_2=5ms$ $v_2=?$

STEP 2: FINDING VELOCITY $\left(v\right)$

$Velocity=frequency\times Wavelength$

$v=f\times \lambda$

$v=\frac{\lambda }{T}$

Also given that,

The wavelength of the two waves is the same

So,

$v\alpha \frac{1}{T}$

$\frac{v_1}{v_2}=\frac{T_2}{T_1}$

$\frac{2}{v_2}=\frac{5}{20}$

$v_2=8m{s}^{-1}$

So, the velocity of the second wave is $8m{s}^{-1}$

The ratio of their velocities is

$$\begin{gathered} \left(\frac{v_1}{v_2}\right)=\frac{2}{8} \\ =\frac{1}{4} \end{gathered}$$

Option ‘c’ is the correct answer.