Question

A sound wave of frequency $500Hz$ covers a distance of $1000m$ in $5\text{second}$ between the points $X$ and $Y$. Then the number of waves between $X$ and $Y$ is :

Answer 1

Step 1: Find speed of the sound wave.

Given, distance covered by sound wave in $5sec,L=1000m$

So, speed of the sound wave, $\upsilon =\frac{L}{T}$

$\upsilon =\frac{1000}{5}=200m/s$

Step 2: Find wavelength of the sound wave.

Formula used: $\upsilon =f\lambda$

Given, frequency of the sound wave, $f=500Hz$

Speed of sound wave, $\upsilon =f\lambda$

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

$\lambda =\frac{200}{500}=0.4m$

Step 3: Find number of waves between $X$ and $Y$.

Formula used: $\text{no. of waves}=\frac{L}{\lambda }$

So, number of waves between $X$ and $Y$,

$=\frac{L}{\lambda }=\frac{1000}{0.4}=2500$

Final answer: $2500$