On a sunny day, the sound in the air is 340 m s⁻¹, and 2 tuning forks A & B are sounded simultaneously.  The wavelength of the sounds emitted is 1.5 m and 1.68 m respectively. How many beats will produce per second? (24 beats approx.) 



Given:

Speed of the sound on a sunny day = v = 340 m s⁻¹
Wavelength of tuning fork A = λ₁ = 1.5 m
Wavelength of tuning fork B = Î»₂ = 1.68 Hz

To Find:

The number of beats  = N = ?

Solution:

The number of beats is equal to the difference in frequencies of the two sources (tuning forks), So, we have to find first the frequencies of both tuning forks A & B


The frequency of tuning fork A = f₁ = `\frac {v}{λ₁}`


f₁ = `\frac {340 m s⁻¹}{1.5 m}`

f₁ = 226.7 Hz

and the frequency of tuning fork B = f₂ = `\frac {v}{λ₁}`


f₂ = `\frac {340 m s⁻¹}{1.68 m}`

f₂ = 202.4 Hz

Now the number of beats

N = f₁ - f₂ = 226.7 Hz - 202.4 Hz = 24.3 beats 

N = 24 beats. ---------------Ans,




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