Question

Two waves are described by the equations:

$y_{1}=Acos \left(0.5 \, \pi x - 100 \pi t\right)$

And $y_{2}=Acos \left(0.46 \, \pi x - 92 \pi t\right)$

Here $x$ and $y$ are in $m$ and $t$ is in $s$ .

Find the number of times $y_{1}+y_{2}$ becomes zero per second, at $x \, = \, 0$ .

• A. $46$
• B. $48$
• C. $192$
• D. $100$

Answer 1

Answer: (D)

At $x=0$ , $y=y_{1}+y_{2}=2Acos 96 \, \pi tcos⁡4\pi t$
Frequency of $cos \left(96 \pi t\right)=48Hz$ and that of $cos \left(\right. 4 \pi t\left.\right)$ function is $2Hz$
In one-second cos function becomes zero at 96 times and second at 4 times. Hence net y will become zero 100 times in 1 second.