Acoustics: Amplitude/frequency/area in regards to sound power

[cb88bear]

I really don't understand this problem at all...my thoughts were that for:
a) you triple the area, sound power would be greater
b) you double the frequency, the period it takes for the sound power to generate is cut in half
c) if you triple the amplitude, the output would be louder
d) you need a large sized loudspeaker to handle the amount of power generated
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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) If the amplitude and frequency are kept the same, but the area of the sound board is tripled, the sound power radiated will be increased by a factor of nine (3x3). b) If the amplitude and area are kept the same, but the frequency of the sound board is doubled, the sound power radiated will be increased by a factor of four (2x2). c) If you triple the amplitude of the vibration of the sound board (changing nothing else), the sound power output will be increased by a factor of nine (3x3). d) The large size of woofer loudspeakers is explained by the fact that the power output for sound radiation increases as the area of the soundboard increases. A larger sound board allows for more sound waves to be generated, resulting in a louder sound output. Additionally, the larger size of woofer loudspeakers also allows for a greater amplitude of vibration, resulting in an even louder sound output.

 

[nlightner]

I can provide some clarification and explanation regarding the concepts of amplitude, frequency, and area in relation to sound power.

Firstly, amplitude refers to the maximum displacement of a vibrating object, such as a sound board. In other words, it measures the strength or intensity of the vibration. Frequency, on the other hand, refers to the number of vibrations or cycles per second and is measured in Hertz (Hz).

Now, let's consider the formula provided for calculating the sound power radiated from a sound board. As you can see, the power is directly proportional to the area (AREA) of the sound board, the square of the amplitude (A^2), and the square of the frequency (f^2). This means that if any of these variables are increased, the sound power will also increase.

a) If the amplitude and frequency are kept the same, but the frequency of the sound board is tripled, the sound power radiated will also triple. This is because the frequency is squared in the formula, meaning that even a small increase in frequency can have a significant impact on the sound power.

b) Similarly, if the amplitude and area are kept the same, but the frequency is doubled, the sound power will increase by a factor of four (2^2) because both the frequency and the area are squared in the formula.

c) If the amplitude is tripled while keeping the frequency and area constant, the sound power output will increase by a factor of nine (3^2). This is because the amplitude is squared in the formula, meaning that even a small increase in amplitude can greatly impact the sound power.

d) The formula does not directly explain the need for large-sized loudspeakers. However, we can infer that a larger area (AREA) would result in a higher sound power output, which is desirable for a loudspeaker. Additionally, a larger loudspeaker would also have a larger amplitude (A) due to its larger size and thus, would be able to produce a louder sound.

I hope this helps to clarify the concepts of amplitude, frequency, and area in relation to sound power. Remember, these variables are all interconnected and can greatly impact the strength and intensity of sound.