Question

Two waves y1=0.25 sin 316tand y2 =0.25sin 310t are travelling in same direction . The number of beat produced per second will be .

Answer 1

Answer: The number of beat produced per second will be $\dfrac{3}{\pi}$.

Explanation:

Given that,

Two waves are travelling in same direction.

$y_{1}= 0.25\ sin\ 316t$

$y_{2}= 0.25\ sin\ 310t$

We know that,

The general equation is

$y = a\ sin\omega t$

Frequency of wave is

$f = \dfrac{\omega}{2\pi}$

Therefore, for first wave

$f_{1}=\dfrac{\omega}{2\pi}$

For second wave

$f_{2}= \dfrac{\omega}{2\pi}$

The number of beat heard per second is

$f_{b} = f_{1}-f_{2}$

$f_{b}= \dfrac{\omega_{1}}{2\pi}-\dfrac{\omega_{2}}{2\pi}$

$f_{b}= \dfrac{316}{2\pi}-\dfrac{310}{2\pi}$

$f_{b}= \dfrac{3}{\pi}$

Hence, The number of beat produced per second will be $\dfrac{3}{\pi}$.