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A sound wave travels at $340m{{s}^{-1}}$. How far from the source the wave has travelled after $0.5s$

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Last updated date: 03rd Mar 2024
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IVSAT 2024
Answer
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Hint: The sound travels through vibrations and it cannot travel without a medium. The speed of the sound is the distance travelled per unit time. Substituting given values in the formula for speed, the distance travelled from the source can be calculated. Convert the units, if required.

Formula used:
$s=\dfrac{d}{t}$

Complete answer:
The sound is a mechanical wave. It requires a medium to travel. The sound travels through a medium as propagation of vibrations. The molecules of the medium undergo compressions and rarefactions and they are transferred to the other molecules in contact. The medium decides the speed of sound.
The speed is given by
$s=\dfrac{d}{t}$
Here, $s$ is the speed
$d$ is the distance
$t$ is the time taken
Given, speed of sound is $340m{{s}^{-1}}$, time taken = $0.5s$
Substituting given values in the above equation, we can calculate distance travelled, therefore,
$\begin{align}
  & 340=\dfrac{d}{0.5} \\
 & \Rightarrow d=340\times 0.5 \\
 & \Rightarrow d=170m \\
\end{align}$
The distance covered by the sound is $170m$.
Therefore, the sound travels a distance of $170m$ in $0.5s$.

Additional Information:
The sounds which have frequencies more than 20 Hz and less than 20,000 Hz only are audible to humans and are known as audible sounds. Sounds having frequency less than 20 Hz are known as infrasonic sounds while sounds having frequency more than 20,000 Hz are known as ultrasonic sounds.

Note:
Sounds are also known as longitudinal waves. The sounds travel fastest in solids and slowest in gases. The regions where high pressures are developed are known as compressions and the regions where low pressures are developed are known as rarefactions. Sounds are differentiated on the basis of different properties like frequency, amplitude, pitch etc.
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