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Answer :
Final answer:
[tex]f_h_i_g_h[/tex] = 600 x (346.2 + 0) / (346.2 + 10.49) = 609 Hz [tex]f_l_o_w[/tex] = 600 x (346.2 - 0) / (346.2 - 10.49) = 577 Hz Therefore, the highest frequency heard by the student is 609 Hz, and the lowest frequency heard is 577 Hz.
Explanation:
The frequency of the sound generator is 600 Hz, and it is tied to a rope of length 1.0 m and whirled around the professor's head in a horizontal circle at 100 rpm. The highest and lowest frequencies heard by a student in the classroom can be found using the Doppler effect equation. The Doppler effect equation is given as follows: f' = f(v ± v₀) / (v ± v_s), where,f' is the observed frequency, f is the emitted frequency, v is the speed of sound, v₀ is the velocity of the observer, [tex]v_s[/tex] is the velocity of the source of the sound. The highest frequency will be heard when the generator is moving towards the student, and the lowest frequency will be heard when the generator is moving away from the student. We know that the velocity of the sound is given by: v = √(γRT),where γ is the adiabatic constant, R is the universal gas constant, and T is the temperature of the room. We can assume γ to be 1.4 for air, and R to be 8.31 J/mol.K. At a temperature of 20∘C or 293 K, we have: v = √(1.4 x 8.31 x 293) = 346.2 m/s The velocity of the source can be found by: [tex]v_s[/tex] = ωr,where ω is the angular velocity and r is the radius of the circle. The radius of the circle is given as 1.0 m. The angular velocity can be found by:ω = 2πf, where f is the frequency of rotation of the rope. We are given that the frequency of rotation is 100 rpm, which can be converted to 100/60 Hz = 1.67 Hz. Therefore,ω = 2π x 1.67 = 10.49 rad/s. Substituting the values into the equation gives: [tex]v_s[/tex] = ωr = 10.49 x 1.0 = 10.49 m/s The velocity of the observer is assumed to be zero because the student is stationary in the classroom. Substituting the values into the Doppler effect equation gives: [tex]f_h_i_g_h[/tex] = 600 x (346.2 + 0) / (346.2 + 10.49) = 609 Hz [tex]f_l_o_w[/tex] = 600 x (346.2 - 0) / (346.2 - 10.49) = 577 Hz Therefore, the highest frequency heard by the student is 609 Hz, and the lowest frequency heard is 577 Hz.
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