Question

Find out the approximate frequency at which maximum intensity is detected by observer O, if velocity of sound = $340m/s$ and frequency range of source is $2000Hz$ to $5000Hz$.

• A. 3350 Hz
• B. 4250 Hz
• C. 2900 Hz
• D. 3778 Hz

Answer 1

The correct option is B 4250 Hz

For constructive interference,
path difference = integral multiple of wavelength
Path difference = $P_1-P_2$
$P_1=10+20+10=40cm$
$P_2=\sqrt{{10}^2+{20}^2}+10=10+10\sqrt{5}\approx 32cm$
$\Delta x=40-32=8cm$
for constructive interference
$p.d=\Delta x=n\lambda$
$8=n\times \frac{u}{\left(frequency\right)}frequency=n\times \frac{u}{8\times {10}^{-2}}=\frac{n\times 340}{8}\times 100=n\times 4250=1\times 4250=4250Hz$