Question

Two tuning forks have frequencies 450Hz and 454Hz respectively. On sounding these together, the time interval between successive maximum intensities will be:
A) $\dfrac{1}{4}second$
B) $\dfrac{1}{2}second$
C) $1 second$
D) $2 second$

Answer 1

Hint: Here indirectly beat frequency is asked.
The beat is a word used for sound waves. The beat frequency is the difference in frequency of two waves. It is because of constructive and destructive interference.
Beat frequency gives us no maxima in beat and its time period gives us a time interval between two successive maxima.

Complete step by step solution:
When two waves of nearly equal frequencies traveling in a medium along the same direction meet at a point, beats are produced. When two sound waves of dissimilar frequency approach your ear, the alternating productive and damaging interference causes the sound to be alternatively loud and soft this is a phenomenon, which is termed as beating.
The beat frequency is equal to the complete value of the alteration in the frequency of the two waves. The count of beats per second is equivalent to the difference in frequencies of two waves is called beat frequency.
Beat Frequency Formula:
\[{f_b} = \left| {{f_2} - {f_1}} \right|\]
Where,
${f_b}$ is the beat frequency
${f_1}$ frequency of the first tuning fork
${f_2}$frequency of the second fork
So, the beat frequency will be,
Given data is
$
  {f_1} = 450Hz \\
  {f_2} = 454Hz$
So, the beat frequency will be
\[
  \because {f_b} = \left| {{f_2} - {f_1}} \right|\, \\
  \therefore {f_b} = \left| {454 - 450} \right| \\
   \Rightarrow {f_b} = 4Hz
 \]
Now as we know that the time period is the reciprocal of the frequency
So, the beat time period will be \[T = \dfrac{1}{{{f_b}}}\]
$T = \dfrac{1}{4} seconds$

Final answer is (A), the time interval between two maxima will be $\dfrac{1}{4}\sec.$

Note: The beat frequency gives the no of maxima in the beat.
Whenever two waves of different frequencies are imposed over each other they produce beats.
There is a lower difference between the frequencies of two waves; the waves strike our eardrum at a small interval of time; this phenomena of two maxima striking our eardrums in a nearly low time interval leads to the production of beats.