Question

Calculate the time taken by a sound wave of frequency 1000 Hz and wavelength 50 cm to travel a distance of 500 m.
A.) 1 s
B.) 3 s
C.) 6 s
D.) 12 s

Answer 1

Hint: The product of the frequency and the wavelength of a wave gives the velocity of the wave in a particular medium. So, if we know the velocity of the wave in a medium, we can calculate the time taken to travel a particular distance d. The time taken will be the distance travelled by the wave divided by the velocity of the wave in the medium.

Complete step-by-step answer:
In the problem, we are given a sound wave of frequency 1000 Hz and having a wavelength of 50 cm. The velocity of a sound wave in a particular medium is determined by the frequency and wavelength of the sound wave in that particular medium. The product of the frequency and the wavelength of a wave gives the velocity of the wave in a particular medium.

So, the velocity of the wave is, $\text{v}=\lambda \upsilon$

Where $\lambda$ is the wavelength and $\upsilon$ is the frequency.
Substituting the values of wavelength and frequency in the above equation, we get,

$\text{v}=(1000Hz)\times \left( 0.5m \right)$
$\therefore \text{v}=500\text{ m/s}$

So, the velocity of the wave in the medium is $\text{v}=500\text{ m/s}$.

It is given that the sound wave travels a distance of 500 m. So, the time taken by the sound wave to travel this distance can be found out by the distance travelled by the wave divided by the velocity of the wave in the medium.

$\text{Time(t)}=\dfrac{\text{Distance}}{\text{Velocity}}$
$t=\dfrac{500m}{500m/s}$
$\therefore t=1\text{ second}$

So, the time taken by the sound wave to travel a distance of 500 m is 1 second.

So, the answer to the question is the option(A).

Note: Waves are of two types, 1) Transverse waves and 2) Longitudinal Waves

There are crests and troughs present in transverse waves while compressions and rarefactions are present in longitudinal waves.
While the wavelength in a transverse wave is the distance between two consecutive troughs or crests, the wavelength in longitudinal waves is defined as the distance between two consecutive compressions or rarefactions.
Sound Waves are usually longitudinal waves while the electromagnetic wave like light is a transverse wave.
The frequency of a wave is defined as the number of vibrations per second. Its SI unit is Hertz (Hz).