Question

𝑆1 and 𝑆2 are two identical sound sources of frequency 656 Hz. The source 𝑆1 is located at 𝑂 and 𝑆2 moves anti-clockwise with a uniform speed of 4$\sqrt{2}$ ms-1 on a circular path around 𝑂, as shown in the figure. There are three points 𝑃, 𝑄 and 𝑅 on this path such that 𝑃 and 𝑅 are diametrically opposite while 𝑄 is equidistant from them. A sound detector is placed at point 𝑃. The source 𝑆1 can move along the direction 𝑂𝑃. [Given: The speed of sound in air is 324 ms-1].

Consider both sources emitting sound. When 𝑆2 is at 𝑅 and 𝑆1 approaches the detector with a speed 4 m s−1 , the beat frequency measured by the detector is _______Hz

Answer 1

f0 = 656 Hz
v = 324 m/s Frequency heard due to movement of (S1)
$f_1=(\frac{v}{v-u_s})f_0$

$f_1=\frac{324}{3520}\times656$

And frequency heard due to movement of (S2)
f2 = 656 Hz
∴ Beat frequency $Δ f = f_1 – f_2$
$=656(\frac{324}{320}-1)$

$Δ f = 8.2$