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Two sound waves with amplitude 4 cm and...

Two sound waves with amplitude ` 4 cm and 3 cm` interfere with a phase difference of
a. `0` b. `pi//3` c. `pi//2` d. `pi`
Find the resultant amplitude in each case.

A

7 cm, `root`37 cm, 4 cm, 2 cm

B

7 cm, 5 cm, `root`35 cm, 8 cm

C

9 cm, `root`38 cm, 7 cm, 5 cm

D

7 cm, `root`37 cm, 5 cm, 1 cm

Text Solution

Verified by Experts

The correct Answer is:
D
Given `A_(1) = 4 cm and A_(2) = 3 cm`
a. When two vectors act along the same direction , their resultant is simply the sum of the magnitudes of the two vectors , so
`A = A_(1) + A_(2) = 4 + 3 cm = 7 cm`
b. Using `A = sqrt (A_(1)^(2) + A_(2)^(2) + 2A_(1) A_(2) cos delta)`,
we have
`A = sqrt( 4^(2) + 3^(2) + 2 xx 4 xx 3 xx cos (pi)/(3)) = sqrt( 16 + 9 + 12) sqrt( 37)`
`:.` The reultant amplitude is `sqrt(37) cm`.
c. The resultant of two perpendicular vectors `A_(1) and A_(2)` is given by
`sqrt(A_(1)^(2) + A_(2)^(2))` , `[:gt cos (pi//2) = 0]`
`A = sqrt( 4^(2) + 3^(2)) cm = 5 cm`
d. The resultant of two vectors in opposite direction is simply the difference in magnitudes between the two vectors , so ,
`A = A_(1) - A_(2) = 4 - 3 cm = 1 cm`
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