Question

What is the distance traveled by sound in the air when a tuning fork of frequency $256Hz$ completes 25 vibrates? The speed of sound in air is $343m{s^{ - 1}}$ .

Answer 1

Hint
If the given values can be altered to our convenience we can solve this problem without any difficulty. The definition of frequency and the distance formula can be used to solve this problem with ease.
$\Rightarrow f = \dfrac{1}{T}$
Frequency, $f$, is the number of oscillations in one unit of time, $T$ .
Distance = speed $\times$ time.

Complete step by step answer
We already know that frequency, $f$, is the number of oscillations in one unit of time, $T$ .
From the equation of frequency, we can find the equation of time as,
$\Rightarrow T = \dfrac{1}{f}$ .
Therefore, the time taken for one oscillation will be,
$\Rightarrow T = \dfrac{1}{{256}}$
We can find the time taken for 25 oscillations in the same way.
$\Rightarrow T = \dfrac{{25}}{{256}}$.
And, we have been given the speed of sound in air as $343m{s^{ - 1}}$ .
We have what we need to substitute in the formula to find the distance traveled, so now we can move forward to find the answer.
Distance travelled $= \dfrac{{343\times 25}}{{256}} = 33.5m$.

Note
The speed of sound changes depending on the medium it is traveling in, in most of the solids the speed of sound can increase as high as $5960m{s^{ - 1}}$. Sound always travels through a medium, which means that sound does not travel in a vacuum.
The Doppler Effect is the change in frequency of the wave in relation to an observer who is moving relative to the wave source. While solving the problem we have to take care that we take the time for 25 oscillations and not for 1 oscillation.