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 42\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].
𝑆1 and 𝑆2 are two identical sound sources of frequency 656 Hz
Consider both sources emitting sound. When 𝑆2 is at 𝑅 and 𝑆1 approaches the detector with a speed 4 m sβˆ’1 , the beat frequency measured by the detector is _______Hz

Updated On: May 1, 2024
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Correct Answer: 8 - 8.4

Solution and Explanation

𝑆1 and 𝑆2 are two identical sound sources of frequency 656 Hz
f0 = 656 Hz 
v = 324 m/s Frequency heard due to movement of (S1)
f1=(vvβˆ’us)f0f_1=(\frac{v}{v-u_s})f_0

f1=3243520Γ—656f_1=\frac{324}{3520}\times656

And frequency heard due to movement of (S2
f2 = 656 Hz   
∴ Beat frequency Ξ”f=f1–f2 Ξ” f = f_1 – f_2 
=656(324320βˆ’1)=656(\frac{324}{320}-1)

Ξ”f=8.2Ξ” f = 8.2

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