x1=12 sin(.484π t-7π x.) and x2=12 sin(.480π t-7π x.) represent the equation of two sound waves and x and t are in metre and second. Beat frequency (in Hz ) produced by these two waves is

Question

x1=12 sin(.484π t-7π x.) and x2=12 sin(.480π t-7π x.) represent the equation of two sound waves and x and t are in metre and second. Beat frequency (in Hz ) produced by these two waves is (A) 4 (B) 3 (C) 2 (D) 1

Tardigrade Admin · Accepted Answer

x1=12sin(.484π t-7π x.) =12sin2π (242 t - (7 x/2)) ∴ frequency n1=242Hz x2=12sin(.480π t-7π x.) =12sin2π (240 t - (7 x/2)) ∴ frequency n2=240Hz Beat frequency =n1-n2=2

Q. $x_{1} = 12 s in (484 π t - 7 π x)$ and $x_{2} = 12 s in (480 π t - 7 π x)$ represent the equation of two sound waves and $x$ and $t$ are in metre and second. Beat frequency (in $Hz$ ) produced by these two waves is

$4$

$3$

$2$

$1$

$x_{1} = 12 s in (484 π t - 7 π x)$
$= 12 s in 2 π (242 t - \frac{7 x}{2})$
$∴$ frequency $n_{1} = 242 Hz$
$x_{2} = 12 s in (480 π t - 7 π x)$
$= 12 s in 2 π (240 t - \frac{7 x}{2})$
$∴$ frequency $n_{2} = 240 Hz$
Beat frequency $= n_{1} - n_{2} = 2$

Q. x1​=12sin(484πt−7πx) and x2​=12sin(480πt−7πx) represent the equation of two sound waves and x and t are in metre and second. Beat frequency (in Hz ) produced by these two waves is

4

3

2

1

x1​=12sin(484πt−7πx) =12sin2π(242t−27x​) ∴ frequency n1​=242Hz x2​=12sin(480πt−7πx) =12sin2π(240t−27x​) ∴ frequency n2​=240Hz Beat frequency =n1​−n2​=2

Q. $x_{1} = 12 s in (484 π t - 7 π x)$ and $x_{2} = 12 s in (480 π t - 7 π x)$ represent the equation of two sound waves and $x$ and $t$ are in metre and second. Beat frequency (in $Hz$ ) produced by these two waves is

$4$

$3$

$2$

$1$

$x_{1} = 12 s in (484 π t - 7 π x)$
$= 12 s in 2 π (242 t - \frac{7 x}{2})$
$∴$ frequency $n_{1} = 242 Hz$
$x_{2} = 12 s in (480 π t - 7 π x)$
$= 12 s in 2 π (240 t - \frac{7 x}{2})$
$∴$ frequency $n_{2} = 240 Hz$
Beat frequency $= n_{1} - n_{2} = 2$