Question

Two waves of wavelength $1.00m$ and $1.01m$ produces $10beats$ in $3s$. What is the velocity of the wave?

• A. $150m/s$
• B. $115.2m/s$
• C. $336.6m/s$
• D. $200m/s$

Answer 1

The correct option is C

$336.6m/s$

Step 1: Given

Wavelength of first wave: ${\lambda }_1=1m$

Wavelength of second wave: ${\lambda }_2=1.01m$

Number of beats: $n=10$

Time for 10 beats: $t=3s$

Step 2: Formula Used

$frequency=\frac{Numberofbeats}{Timetaken}$

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

Step 3: Find the frequency

Calculate the frequency using the formula

$$\begin{gathered} f=\frac{n}{t} \\ =\frac{10}{3}Hz \end{gathered}$$

Step 4: Find the velocity of the wave

Calculate the velocity by taking the difference of the frequencies and substituting the values

$$\begin{gathered} f_1-f_2=\frac{v}{{\lambda }_1}-\frac{v}{{\lambda }_2} \\ \Rightarrow \frac{10}{3}=v\left(\frac{{\lambda }_2-{\lambda }_1}{{\lambda }_1{\lambda }_2}\right) \\ \Rightarrow \frac{10}{3}=v\left(\frac{1.01-1}{1\times 1.01}\right) \\ \Rightarrow v=\frac{10}{3}\times \frac{1.01}{0.01} \\ \Rightarrow v=336.6m/s \end{gathered}$$

Hence, the velocity of the wave is $336.6m/s$.