wave_mechanics interference_and_superposition_of_waves Question 6
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
Options:
A) 0.7 mm
B) 0.1 mm
C) 0.2 mm
D) 0.5 mm
Show Answer
Answer:
Correct Answer: D
Solution:
$ \lambda =\frac{v}{n}=\frac{350}{350}=1m $ =100 cm Also path difference $ (\Delta x) $ between the waves at the point of observation is $ AP-BP=25cm $ .
Hence
Therefore $ \Delta \varphi =\frac{2\pi }{\lambda }(\Delta x)=\frac{2\pi }{1}\times ( \frac{25}{100} )=\frac{\pi }{2} $
Therefore $ A=\sqrt{{{(a _{1})}^{2}}+{{(a _{2})}^{2}}} $
$ = $
$ \sqrt{{{(0.3)}^{2}}+{{(0.4)}^{2}}} $ = 0.5 $ mm $
BETA
