 #1
custner
 3
 0
 Homework Statement:

This for my first university course in waves.
p=105 kPa and T= 300 K. We are in air. A loudspeaker with a circular membrane of diameter 1 mm sends out sound. At a distance of 10 meters, the sound intensity level is 50 dB. What is the maximum velocity that the loudspeakers membrane vibrates with?
 Relevant Equations:

Z=p*sqrt(gamma*M/(R*T))
dB = 10*log(I/I_0)
I=0.5∗Z∗(v_(max))^2
My attempt:
p and T allows us to calculate ##Z=402 \frac{kg}{sm^2}## using ## Z=p*\sqrt(\frac{\gamma*M}{R*T})## . The sound intensity level at 10 meters allows us to calculate the intensity at 10 meters to be I=10``````^{7} W/m^2 using ##50 = 10*log(I/I_0)##. Then, using the formula ##I=0.5∗Z∗v_{max}^2##, which gives ##v_{max}=2.23∗10^{−5} m/s##
My question:
Sound waves are spherical waves, but the expression ##I=0.5∗Z∗v_{max}^2## is (from what I understand) for planar waves. This makes me think that it is incorrect to use it since sound waves (I think?) are spherical waves. Is it still correct to use it for sound waves? Because the answer to me feels very small
p and T allows us to calculate ##Z=402 \frac{kg}{sm^2}## using ## Z=p*\sqrt(\frac{\gamma*M}{R*T})## . The sound intensity level at 10 meters allows us to calculate the intensity at 10 meters to be I=10``````^{7} W/m^2 using ##50 = 10*log(I/I_0)##. Then, using the formula ##I=0.5∗Z∗v_{max}^2##, which gives ##v_{max}=2.23∗10^{−5} m/s##
My question:
Sound waves are spherical waves, but the expression ##I=0.5∗Z∗v_{max}^2## is (from what I understand) for planar waves. This makes me think that it is incorrect to use it since sound waves (I think?) are spherical waves. Is it still correct to use it for sound waves? Because the answer to me feels very small
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