Cindy gets angry at Ronit and ties her to a chair facing a 10 W speaker that is
ID: 1376632 • Letter: C
Question
Cindy gets angry at Ronit and ties her to a chair facing a 10 W speaker that is blasting Miley Cyrus 10 meters away. The speaker is also attached to a spring that has a spring constant of 1,000 N/m and to make the music that much more irriating Cindy hits the speaker to have it oscillate back and forth. To keep her sanity Ronit does physics problems in her head. She notices that the loudest the songs gets is 105 dB, and the Miley Cryrus' annoyting 400 Hz scream at most becomes an annoying 503.9 Hz scream. What is the mass of the speaker? HINT: Must use doppler method to recieve full credit.
Explanation / Answer
Let speed of sound = Vs = 330 m/s
using dopplers effect
Fnew = Fold (Vs/Vs - Vc)
503.9 = 400 (330/ 330 - Vc)
Vc = 91.85 m/s = Maximum Velocity of chair
Now, maximun velocity of chair occurs when spring is not stretched.
Also, using maximun intensity,
dB = 10log[I/Io]
105 = 10log[(P/4*pi*r^2) / Io]
105 = 10log[10/4 * 3.142* r^2 * 10^-12]
r = 5.016 m
using energy conservation equation:
PE = KE
1/2 x k x r^2 = 1/2 x m x Vc^2
1/2 x 1000 x 5.016^2 = 1/2 x m x 91.85^2
m = 2.98 kg = ANSWER