A tuning fork A of frequency 384 Hz gives 6 beats in 2 second when sounded with another tuning fork B. The frequency of B could be?

Concept:

• When two sound waves of slightly different frequencies, travelling in a medium along the same direction, superimpose on each other, the intensity of the resultant sound at a particular position rises and falls regularly with time.
• This phenomenon of regular variation in the intensity of sound with time at a particular position is called beats.
• Beat frequency: The number of beats produced per second is called a beat frequency.

Beat frequency = number of beats/sec

• If n₁ and n₂ are the frequency of two sources, then the difference in frequencies of two sources

m = (n₁ - n₂) or (n₂ – n₁)

Where m = beat frequency

Calculation:

Given Fork A = 384 Hz, 6 beats are produced in 2 seconds

Thus beat frequency

Beat frequency  b = ∣f_A​−f_B​∣

∴ 3 = ∣384−f_B​∣

Thus   f_B​ = 384 – 3 = 381 Hz  or   f_B​ = 384 + 3 = 387 Hz

So, The frequency of B can either be 381 Hz or  387 Hz