A sound wave has frequency of $5\mathrm{kHz}$ and wavelength $50 \mathrm{cm}$. Then distance travelled by sound in $4\sec$. (in $\mathrm{km}$ ) will be

Solution:

The wavelength is the distance or length between two successive crests or troughs of a wave. The frequency (f) of a repeated event is the number of occurrences per unit of time. Hertz _(Hz) is its Sl unit. Velocity (v) is defined as the rate of change of a body's displacement with respect to time. metre per second $\left({\mathrm{ms}}^{-1}\right)$ is the SI unit.

We know that speed formula in terms of wavelength and frequency
Speed (v)= wavelength$\left(\lambda \right)\times$frequency (f).
According to question given that,
Wavelength $\left(\lambda \right)=50 \mathrm{cm}=50/100 \mathrm{m}=0.5 \mathrm{m}$
Frequency $\left(f\right)=5\mathrm{kHz}=5000 \mathrm{Hz}$
Speed $\left(v\right)=f\times \lambda$
$\Rightarrow V=5000\times 0.5=2500 \mathrm{m}/\mathrm{s}$

The distance travelled in$4\sec =$speed$\times$time $=2500\times 4=10000 \mathrm{m}=10 \mathrm{km}$
Hence option 1 is correct.