Question

Two sources of sound A and B produces the wave of 350 Hz, 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 0.3 mm and 0.4 mm, then the resultant amplitude of the point P will be when AP - BP = 25 cm and the velocity of sound is 350 m/sec

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

Answer 1

The correct option is D

0.5 mm

$\lambda =\frac{v}{n}=\frac{350}{350}=1m=100cm$

Also path difference $\left(△x\right)$ between the waves at the point of observation is $AP-BP=25cm$. Hence

$\Rightarrow △\varphi =\frac{2\pi }{\lambda }\left(△x\right)=\frac{2\pi }{1}\times ⟮\frac{25}{100}⟯=\frac{\pi }{2}$

$\Rightarrow A=\sqrt{(a_1{)}^2+(a_2{)}^2}=\sqrt{(0.3{)}^2+(0.4{)}^2}=0.5mm$