Question

What is your observation when two sources are emitting sound with frequency 499 Hz and 501 Hz
A. frequency of 500 Hz is heard with change in intensity taking place twice.
B. frequency of 500 Hz is heard with change in intensity once.
C. frequency of 2 Hz is heard with change in intensity taking place once.
D. frequency of 2 Hz is heard with change in intensity take place twice.

Answer 1

Hint: To answer this problem, you should know when many sounds of different frequencies are emitted together, at that time the average of all the frequencies can be heard. In this case, there are two frequencies, so take the average of these frequencies. The obtained frequency will be the frequency which can be heard. Now, the difference between those two frequencies will tell us how many times the intensity will change.

Complete step-by-step answer:
Let ${f}_{1}$ and ${f}_{2}$ be the two frequencies
Given: ${f}_{1}$ = 499 Hz
            ${f}_{2}$ = 501 Hz
Frequency heard will be the average of both the frequencies which can be written as,
$f = \dfrac {{f}_{1} + {f}_{2}}{2}$
Substituting the values in above equation we get,
$F = \dfrac {499 + 501}{2}$
$\Rightarrow F = \dfrac {1000}{2}$
$\Rightarrow F = 500 Hz$
Difference between the frequencies of both the sounds is 2 Hz. Thus, the change in frequency will take place twice.
Hence, when two sources are emitting sound with frequency 499 Hz and 501 Hz, frequency of 500 Hz is heard with change in intensity taking place twice.

So, the correct answer is “Option A”.

Note: Students must know that if both the frequencies are 180° out of phase then, the frequencies will cancel out. Thus, we might not be able to hear anything. This is how noise-cancellation devices work. But, the cancellation may not be perfect. Still there may be frequencies that can be heard. It is impossible to cancel these frequencies completely as both the frequencies are emitted from different sources.