Question

The frequency of a tuning fork is 256 Hz and velocity of sound in air is $ 350m/s $. Find the distance covered by the wave when the fork completes 16 vibrations.

Answer 1

Hint
For solving this question, we need to calculate the time required by the fork to complete 16 vibrations. Further, since we know the velocity of the sound waves, we can calculate the distance covered by the wave.
Time $ \left( t \right) $ required for $ n $ number of vibrations is given by
$\Rightarrow t = \dfrac{n}{f} $ where $ f $ is the frequency.
Distance $ \left( d \right) $ travelled by the wave, $ d = v \times t $ , where $ v $ is the velocity of the sound waves.

Complete step by step answer
Here, it is given the frequency of the tuning fork, $ f = 256Hz $ , and the velocity of the sound in air, $ v = 350m/s $ . We also know that the total number of vibrations per unit time is the frequency. Therefore, from the given data, we can also say that the tuning fork completes 256 vibrations in one second. So, we can calculate the time required for the tuning fork to complete 16 vibrations as,
$\Rightarrow t = \dfrac{{16}}{{256{s^{ - 1}}}} = \dfrac{1}{{16}}s $
So, the tuning fork takes $ \dfrac{1}{{16}} $ seconds to complete 16 vibrations.
Since the velocity of the sound waves in air is given, the distance covered by the wave while the tuning fork completes 16 vibrations can be easily calculated as:
$\Rightarrow d = 350m/s \times \dfrac{1}{{16}}s = 21.875m $
Hence, the answer is $ 21.875m $ .

Note
In the problem the frequency of the tuning fork is given in the units of hertz $ \left( {Hz} \right) $ , but in the solution we have considered it as $ {s^{ - 1}} $ . This is because the frequency is defined as the number of vibrations per second and $ 1Hertz(Hz) = 1vibration/s $ . Therefore, the unit of frequency can also be written as $ {s^{ - 1}} $ .