Question

A wave of frequency $500\text{Hz}$travels between $\text{X}$ and $\text{Y}$, a distance of $600\text{m}$ in $2$ sec. How many wavelength are there in distance $\mathrm{XY}$?

• A. $1000$
• B. $300$
• C. $180$
• D. $2000$

Answer 1

The correct option is A

$1000$

Step 1: Given parameters

Frequency, $\mathrm{f}=500\mathrm{Hz}$

Displacement, $\mathrm{s}=600\mathrm{m}$

Time, $\mathrm{t}=2\mathrm{seconds}$

Step 2: Formula used

The velocity of the wave is given by, $\mathrm{v}=\frac{\mathrm{s}}{\mathrm{t}}$ where $\mathrm{v}$ is the velocity, $\mathrm{s}$ is the displacement, $\mathrm{t}$ is the time.

The wavelength of the wave is given by $\mathrm{\lambda }=\frac{\mathrm{v}}{\mathrm{f}}$

No. of the wavelengths traveled is $\mathrm{N}=\frac{\mathrm{s}}{\mathrm{\lambda }}$

Step 3: Calculating the wavelength

Velocity, $\mathrm{v}=\frac{\mathrm{s}}{\mathrm{t}}$

$\mathrm{v}=\frac{600}{2}$

$\mathrm{v}=300\mathrm{ms}$

wavelength, $\mathrm{\lambda }=\frac{\mathrm{v}}{\mathrm{f}}$

$\mathrm{\lambda }=\frac{300}{500}$

$\mathrm{\lambda }=0.6$ m

No. of the wavelengths traveled, $\mathrm{N}=\frac{\mathrm{s}}{\mathrm{\lambda }}$

$\mathrm{N}=\frac{600}{0.6}$

$\mathrm{N}=1000$

Therefore, distance $\mathrm{XY}$ is equivalent to $1000$ wavelengths.