Question

A point sound source is situated in a medium of bulk modulus $1.6b\times {10}^{5}N/m^2$ . The equation for the wave emitted it is given by $y=Asin(7.5\pi x-300\pi t)$ . Velocity of wave is $\nu$ and the displacement amplitude of the waves received by the observer standing at a distance $5m$ from the source is A . The density of medium is $\rho$ . The pressure amplitude at the observer ear is $30Pa$ . The intensity of wave received by the observer is I . Then

• A. $\rho =1kg/m^3$
• B. $\nu =400m/s$
• C. $A=\frac{{10}^{-4}}{4\pi }$
• D. $I=1W/m^2$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $\rho =1kg/m^3$
B $\nu =400m/s$
C $A=\frac{{10}^{-4}}{4\pi }$

$y=Asin(7.5\pi x-3000\pi t)$
$k=\frac{2\pi }{\lambda }=7.5\pi$ $\Rightarrow \lambda =\frac{2}{7.5}m$
$\omega =2\pi f=3000\pi$ $\Rightarrow f=1500Hz$
$\nu =\frac{2}{7.5}\times 1500=400m/s$
Density
$\rho =B/{\nu }^2=1.6\times {10}^5/(400{)}^2=1kg/m^3$
$(\Delta \rho {)}_{max}=BAk$
The maximum amplitude of the wave is
$A=\frac{(\Delta \rho {)}_{max}}{Bk}=\frac{30}{1.6\times {10}^5\times 7.5\pi }$
$=\frac{10\times {10}^{-5}}{4\pi }=\frac{{10}^{-4}}{4\pi }m$