Two waves are described by the equations: y1=Acos (0.5 π x - 100 π t) And y2=Acos (0.46 π x - 92 π t) Here x and y are in m and t is in s . Find the number of times y1+y2 becomes zero per second, at x = 0 .

Question

Two waves are described by the equations: y1=Acos (0.5 π x - 100 π t) And y2=Acos (0.46 π x - 92 π t) Here x and y are in m and t is in s . Find the number of times y1+y2 becomes zero per second, at x = 0 . (A) 46 (B) 48 (C) 192 (D) 100

Tardigrade Admin · Accepted Answer

At x=0 , y=y1+y2=2Acos 96 π tcos⁡4π t Frequency of cos (96 π t)=48Hz and that of cos (. 4 π t.) 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.

Q. Two waves are described by the equations:

$y_{1} = A cos (0.5 π x - 100 π t)$

And $y_{2} = A cos (0.46 π x - 92 π t)$

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 $x = 0$ .

$46$

$48$

$192$

$100$

At $x = 0$ , $y = y_{1} + y_{2} = 2 A cos 96 π t cos 4 π t$
Frequency of $cos (96 π t) = 48 Hz$ and that of $cos (4 π t)$ function is $2 Hz$
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.

Q. Two waves are described by the equations: y1​=Acos(0.5πx−100πt) And y2​=Acos(0.46πx−92πt) Here x and y are in m and t is in s . Find the number of times y1​+y2​ becomes zero per second, at x=0 .

46

48

192

100