How Does Changing Frequency and Amplitude Affect Sound Power Radiated?

[cb88bear]

Acoustics Homework Question! Please HELP!

We're doing some problems in my acoustics class...and I absolutely don't get this one! HELP PLEASE!

For radiation from a sound board of area AREA, vibrating with amplitude A at frequency f we find power for P radiated:

P=(2.8x10^5 Newton/m^2)((AREA)A^2f^2)/(c))

**Sorry about that formula...i don't know how else to write it on here***
a)If the amplitude and frequency are kept the same, but the frequency of the sound board is tripled, what happens to the sound power radiated?

b) If the amplitude and area are kept the same, but the frequency of the sound board is doubled, what happens to the sound power radiated?

c) If you triple the amplitude of the vibration of the sound board (changing nothing else), how does the sound power output change?

d)How does this formula explain the large size of "woofer" loudspeakers?
PLEASE HELP ME!

 

[jbsteele]

a) The sound power radiated will be nine times more. b) The sound power radiated will be four times more. c) The sound power output will be nine times more.d) The large size of "woofer" loudspeakers is due to the larger area of the speaker that allows for the production of more sound power. The larger area increases the amount of energy that can be radiated, and this is reflected in the formula, as the sound power output is proportional to the area of the soundboard.

 

[nlightner]

Hi there,

I can definitely help you with these questions. Let's break down the formula first:

P = (2.8x10^5 Newton/m^2) * (AREA) * (A^2) * (f^2) / c

P = sound power radiated (in watts)
2.8x10^5 Newton/m^2 = constant value
AREA = area of the sound board (in m^2)
A = amplitude of vibration (in m)
f = frequency of vibration (in Hz)
c = speed of sound (in m/s)

Now, let's answer the questions:

a) If the frequency of the sound board is tripled, the sound power radiated (P) will increase by a factor of 9. This is because the frequency (f) is squared in the formula. So, if f is tripled, f^2 will be 9 times the original value.

b) If the frequency is doubled, the sound power radiated will increase by a factor of 4. This is because f is squared in the formula. So, if f is doubled, f^2 will be 4 times the original value.

c) If the amplitude is tripled, the sound power output (P) will increase by a factor of 9. This is because the amplitude (A) is squared in the formula. So, if A is tripled, A^2 will be 9 times the original value.

d) The formula explains the large size of "woofer" loudspeakers because the larger the area (AREA) and the amplitude (A), the more sound power (P) can be radiated. This is why woofer speakers are typically larger than other speakers - to produce more sound power.

I hope this helps you understand the questions better. Let me know if you have any other questions or need further clarification. Good luck with your acoustics class!