A speaker emits sound equally in all directions at frequency of 72 Hz. a distanc

Question

A speaker emits sound equally in all directions at frequency of 72 Hz. a distance of 30.0 [m] the intensity of this sound is 7.00 times 10^-8 W/m^2. Assume that there are no echoes and no objects to block the sound. Find the total sound power emitted by the speaker _. At what distance from the speaker is the intensity level equal to 30.0 decibels? _. How many joules per second of sound energy enter a 2.00cm diameter circular opening that is facing the speaker and is 30.0 meters away from the speaker? _ If the sound power emitted by the speaker remains the same hut the frequency of the sound increases, state whether the following values will increase, decrease, or remain the same. Assume that there are no changes in the properties of the air. Amplitude of the pressure wave 30.0 [m] from the speaker will_. Amplitude of the displacement wave 30.0 [m] from the speaker will_.

Explanation / Answer

Sound emitted in all direcitons equally
frequency,f = 72 Hz
a) at distance r = 30 m, I = 7*10^-8 W/m^2
Now, Power P = I*A ( I is intensity, A is area)
so, P = I = 7*10^-8 * 4*pi*r^2
P = 7.9128*10^-4 W
b) If intensity in decibles = Ib
Ib = 10*log(I/10^-12) [ where I is the inttensity in W/m^2]
Ib = 30 decible = 10log(I/10^-12)
I = 10^-9 W/m^2 = P/4*pi*r^2
r = 250.99 m
c) Power enetering the opening = Net power * projected area/ total area = P(r')^2/4r^2
r = 30 m
r' = 0.02 m
Power = P(0.02)^2/4*30^2 = 8.792*10^-11 W

d) Amplitude of pressure wave does not cahnge with frequency so it would remain the same
Amplitude of displacement wave does not cahnge with frequency so it would remain the same

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