Tag: superposition of waves-1: interference and beats

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Multiple choice physics superposition of waves-1: interference and beats sound as a wave of disturbance vibrations in a tuning fork vibrations in tuning fork

Two sound waves of wavelengths $1\space m$ and $1.01\space m$ produce $10$ beats in $3$ seconds. Then, the velocity of the sound is

  1. $330\space ms^{-1}$
  2. $333.3\space ms^{-1}$
  3. $336.7\space ms^{-1}$

  4. none of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From the formula, $v=f \lambda$

and the velocity of the sound in air is frequency independent.

for two frequencies $f _1$ and $f _2$, wavelengths are $\lambda _1$ 

and $\lambda _2$ , then the beats will be

$f _1-f _2=v\left(\dfrac{1}{\lambda _1}-\dfrac{1}{\lambda _2}\right)=v\left(\dfrac{\lambda _2-\lambda _1}{\lambda _2  \lambda _1}\right)$

$\dfrac{10}{3}=v\left(\dfrac{0.01}{1.0\times 1.01}\right)$

$v=\dfrac{10\times 1.0\times 1.01}{3.0\times 0.01}=336.66\ \text{ms}^{-1}$

Option "C" is correct.