Question

Find the observed intensity level (in dB) when both speakers are on and in phase but the frequency is 85 Hz.

Answer 1

$60=10\log \left(\frac{i_0}{{10}^{-1}}\right)$

$i_0={10}^{-16}w/m^2$

Both speakers have same intensity.

Path difference =$11-8=3m=△x$

$\frac{\lambda }{△x}=\frac{2\pi }{△\varphi }(\lambda =\frac{340}{170}=2m)$

$△\varphi =3\pi$

At $f=85Hz$

$\lambda =4m$

$\frac{4}{3}=\frac{2\pi }{△\varphi }$

$△\varphi =3\pi /2$

Resultant intensity would be=

$4i_0{\cos }^2\left(\varphi /2\right)=2i_0=2\times {10}^{-6}w/m^2$

$dB=10\left[\log \right({10}^6)+\log (2\left)\right]$

$⟹10[6+0.3]$

$⟹63dB$