Question

A sound wave has frequency of 2 kHz and wavelength 35cm. How long will it take to travel $1.5\text{ }km$?

Answer 1

Waves are vibratory disturbance in a medium which carries energy from one point to another point without actual moment of the medium. We are all dependent on sound waves which travel longitudinally in space. Some of the important terms of this type of wave motion include Wavelengths we know the distance from the kinematics point of view as $velocity\times time$. The wave motion distance of a complete wave is described by $'\lambda '$ and it has the same dimensions. When we say a wave vibrates, then the time period taken to complete one vibration is ‘T’.
Number of vibrations completed in 1sec is called frequency.

$\text{frequency}\left( f \right)=\dfrac{1}{\text{Time period}\left( T \right)}\text{Hertz}$
Velocity of the wave is given here by
$v=f\lambda$

Complete answer:
Here wavelength $\lambda =35cm$
$\lambda =\dfrac{35}{100}=0.35$
Frequency given is $f=2kHz$
$f=2000Hz$
Distance travelled $=105km$
$d=1500m$
We know that
$\text{speed of sound}=\text{wavelength}\times \text{frequency}$

& v=\lambda \times f=0.35\times 2000 \\\ & v=700m/s \\\ \end{aligned}$$ We know that speed $$=\dfrac{\text{distance}}{\text{Time}}$$ $$\begin{aligned} & \text{Time}=\dfrac{d}{v} \\\ & T=\dfrac{1500}{700m/s} \\\ \end{aligned}$$ $$T=2.1s$$ Hence time taken by sound is $$2.1s$$ **Note:** Before knowing all the formulas we should know all about the properties of waves. A sound wave needs a medium to propagate. You can't make sound travel in vacuum. We also see in our day to day life that waves show properties of reflection, refraction. You can hear a man screening outside the pool of water when you are in the deep water. Waves also can be superimposed on each other to increase the pitch of the sound data or can be reduced also. These are practical life applications and experiments which you can connect easily with the physics formulas.