wave_mechanics musical_sound Question 4
Question: If the amplitude of sound is doubled and the frequency reduced to one-fourth, the intensity of sound at the same point will be
[CBSE PMT 1992]
Options:
A) Increased by a factor of 2
B) Decreased by a factor of 2
C) Decreased by a factor of 4
D) Unchanged
Show Answer
Answer:
Correct Answer: C
Solution:
$ I=2{{\pi }^{2}}a^{2}n^{2} $
$ v\rho $
Therefore $ I\propto a^{2}n^{2} $
Therefore $ \frac{I _{1}}{I _{2}}={{( \frac{a _{1}}{a _{2}} )}^{2}}\times {{( \frac{n _{1}}{n _{2}} )}^{2}} $
$ ={{( \frac{1}{2} )}^{2}}\times {{( \frac{1}{1/4} )}^{2}}\Rightarrow I _{2}=\frac{I _{1}}{4} $
BETA
