Question

Two sources of sound $A$ and $B$ produces the wave of $350Hz$, they vibrate in the same phase. The particle $P$ is vibrating under the influence of these two waves, if the amplitudes at the point $P$ produced by the two waves is $0.3mm$ and $0.4mm$, then the resultant amplitude of the point $P$ will be when $AP-BP=25cm$ and the velocity of sound is $350m/\sec$

• A. 0.7 mm
• B. 0.1 mm
• C. 0.2 mm
• D. 0.5 mm

Answer 1

Answer: (D)

$\lambda =\frac{v}{n}=\frac{350}{350}=1m=100cm$
Also path difference $(\Delta x)$ between the waves at the point of observation is $AP-BP=25cm$.
Hence $\Rightarrow \Delta \phi =\frac{2\pi }{\lambda }(\Delta x)=\frac{2\pi }{1}\times \left(\frac{25}{100}\right)=\frac{\pi }{2}$
$\Rightarrow A=\sqrt{{\left(a_1\right)}^2+{\left(a_2\right)}^2}$
$=\sqrt{(0.3{)}^2+(0.4{)}^2}=0.5mm$