Two coherent sources of sound, $S_{1}$ and $S_{2}$ , produce sound waves of the same wavelength, $λ = 1$ m, in phase. $S_{1}$ and $S_{2}$ are placed 1.5 m apart (see fig). A listener, located at L, directly in front of $S_{2}$ finds that the intensity is at a minimum when he is 2 m away from $S_{2}$ . The listener moves away from $S_{1}$ , keeping his distance from $S_{2}$ fixed. The adjacent maximum of intensity is observed when the listener is at a distance d from $S_{1}$ . Then, d is :

Moderate

Solution

$\begin{array}{l} A t L : \\ P h a s e d i f f e r e n c e = Δ ϕ = \frac{2 π}{λ} △ x = \frac{2 π}{λ} (S_{1} L - S_{2} L) \\ \Rightarrow Δ ϕ = \frac{2 π}{1} (\sqrt{4 + \frac{9}{4}} - 2) = 2 π (\frac{5}{2} - 2) = π \\ T h i s m e a n s M i n i m a i s f o r m e d . \end{array}$
$\begin{array}{l} N o w a t o t h e r p o s i t i o n, \\ Δ ϕ = \frac{2 π}{1} (d - 2) = 2 π [f o r a d j a c e n t m a x i m a Δ ϕ = 2 π] \end{array}$
$\Rightarrow d = 3 m$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

SCAN ME