Question

A mosquito is sound with its wings at an average rate of $500$ vibrations per $10$ seconds. The frequency of vibration is?

Answer 1

Hint: Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as temporal frequency to emphasize the contrast to spatial frequency, and ordinary frequency to emphasize the contrast to angular frequency.

Formula used:
\[f = \dfrac{1}{T}\]
Where,
$f$ is the frequency and
$T$ is the time period.

Complete step by step solution:
It is given that the rate of vibration is $500$ per $10\sec $
$
  \because T = \dfrac{1}{f} \\
   \Rightarrow T = \dfrac{1}{{\dfrac{{500}}{{10}}}} \\
   \Rightarrow T = \dfrac{1}{{50}} \\
  \therefore f = 50Hz \\
 $
In wave mechanics, any given wave enfolds parameters like- frequency, period, wavelength, amplitude, etc. Frequency is the number of occurrences of a repeating event per unit of time. And its unit is $Hz$.

Additional information:
The symbols most often used for frequency are $(f)$ and the Greek letters nu $\nu $ and omega $(\omega )$. Nu is used more often when specifying electromagnetic waves, such as light, X-rays, and gamma rays. Omega is usually used to describe the angular frequency—that is, how much an object rotates or revolves in radians per unit time. Usually, frequency is expressed in the hertz unit, named in honour of the 19th-century German physicist Heinrich Rudolf Hertz, one hertz being equal to one cycle per second, abbreviated $Hz$ ; $1kHz$ is $1000Hz$, and $1mHz$ is $1000000Hz$. In spectroscopy another unit of frequency, the wavenumber, the number of waves in a unit of distance, is sometimes used.

Note:
In this type of question just do not confuse time period with frequency and then you can easily solve the question. The period is the time taken by an entire cycle of the wave to pass a degree, Frequency is the variety of complete cycles of waves passing a degree in unit time.