Question

A wave of frequency $100Hz$ travels with a velocity of $3m{s}^{-1}$. If the time
period of another wave is $8ms$, then its velocity and also the ratio of their
velocities are _________. (Assume that the wavelength of the two waves is
the same).

• A. $\frac{30}{8}m{s}^{-1},\frac{5}{2}$
• B. $\frac{15}{4}m{s}^{-1},\frac{4}{5}$
• C. $\frac{30}{8}m{s}^{-1},\frac{2}{5}$
• D. None of these

Answer 1

The correct option is B

$\frac{15}{4}m{s}^{-1},\frac{4}{5}$

Step 1: Given Data,

For wave 1,

Frequency = 100 Hz.

Velocity = 3 ms^-1.

For wave 2,

Time period = 8 ms.

Step 2: Solution,

For 1^st wave,

$$\begin{gathered} v=f\lambda \\ \lambda \left(wavelength\right)=\frac{v}{f}=\frac{3}{100}=0.03mor3cm. \end{gathered}$$

The time period of the 2^nd wave is 8 ms,

So frequency is $\frac{1}{Timeperiod}=\frac{1}{8ms}=\frac{1000}{8}=125Hz.$

So velocity is,

$$\begin{gathered} v=f\lambda \\ v=125\times 0.03=\frac{125\times 3}{100}=\frac{15}{4}m{s}^{-1} \end{gathered}$$

Now ratio of their velocity, 1st by 2nd =$\frac{3}{0.03\times 125}=\frac{3\times 100}{3\times 125}=\frac{100}{125}=\frac{4}{5}$

Hence the correct option is (B) $\frac{15}{4}m{s}^{-1},\frac{4}{5}$