Question

The equation of diaplacement due to a sound wave is $s=s_0{\text{sin}}^2(\omega t-kx)$. If the bulk modulus of the medium is $B$, then the equation of pressure variation due to that sound is

• A. $-Bk{s}_0{\cos }^2(\omega t-kx)$
• B. $-Bk{s}_0\sin (2\omega t-2kx)$
• C. $Bk{s}_0\sin (2\omega t-2kx)$
• D. $Bk{s}_0{\cos }^2(\omega t-kx)$

Answer 1

The correct option is C $Bk{s}_0\sin (2\omega t-2kx)$

Given, displacement equation for sound wave, $s=s_0{\sin }^2(\omega t-kx)$

So, pressure variation due to sound,

$P=-B\left(\frac{ds}{dx}\right)$

$P=-B\left(\frac{d}{dx}\right(s_0{\sin }^2(\omega t-kx)\left)\right)$

$P=-B(-k)s_0(2\sin \omega t-kx)\left(\cos \right(\omega t-kx\left)\right)$

$(\text{Using}\sin 2\theta =2\sin \theta \cos \theta )$

$P=Bk{s}_0\sin (2\omega t-2kx)$

Final answer: (a)