A sound wave of frequency 245 Hz travels with the speed of 300 ms -1 along the positive x -axis. Each point of the wave moves to and fro through a total distance of 6 cm. What will be the mathematical expression of this travelling wave ?

Question

A sound wave of frequency 245 Hz travels with the speed of 300 ms -1 along the positive x -axis. Each point of the wave moves to and fro through a total distance of 6 cm. What will be the mathematical expression of this travelling wave ? (A) Y ( x , t )=0.03[ sin 5.1 x -(0.2 × 103) t ] (B) Y ( x , t )=0.06[ sin 5.1 x -(1.5 × 103) t ] (C) Y ( x , t )=0.06[ sin 0.8 x -(0.5 × 103) t ] (D) Y ( x , t )=0.03[ sin 5.1 x -(1.5 × 103) t ]

Tardigrade Admin · Accepted Answer

ω=2 π f =1.5 × 103 A=(6/2)=3 cm =0.03 m

Q. A sound wave of frequency $245 Hz$ travels with the speed of $300 m s^{- 1}$ along the positive $x$ -axis. Each point of the wave moves to and fro through a total distance of $6 c m$ . What will be the mathematical expression of this travelling wave ?

$Y (x, t) = 0.03 [sin 5.1 x - (0.2 \times 1 0^{3}) t]$

$Y (x, t) = 0.06 [sin 5.1 x - (1.5 \times 1 0^{3}) t]$

$Y (x, t) = 0.06 [sin 0.8 x - (0.5 \times 1 0^{3}) t]$

$Y (x, t) = 0.03 [sin 5.1 x - (1.5 \times 1 0^{3}) t]$

$ω = 2 π f$
$= 1.5 \times 1 0^{3}$
$A = \frac{6}{2} = 3 c m = 0.03 m$

Q. A sound wave of frequency 245Hz travels with the speed of 300ms−1 along the positive x -axis. Each point of the wave moves to and fro through a total distance of 6cm. What will be the mathematical expression of this travelling wave ?

Y(x,t)=0.03[sin5.1x−(0.2×103)t]

Y(x,t)=0.06[sin5.1x−(1.5×103)t]

Y(x,t)=0.06[sin0.8x−(0.5×103)t]

Y(x,t)=0.03[sin5.1x−(1.5×103)t]