# Speaker attached to spring

1. Oct 18, 2012

### songoku

1. The problem statement, all variables and given/known data
A block with a speaker bolted to right side of it is put on the table. The left side of the block is connected to a spring having spring constant k and the block is free to oscillate in horizontal direction. The total mass of the block and speaker is m, and the amplitude of this unit's motion is A. The speaker emits sound waves of frequency f and speed of sound is v

a. Determine the highest frequency heard by the person
b. Determine the lowest frequency heard by the person
c. If the maximum sound level heard by the person is β when the speaker is at its closest distance d from him, what is the minimum sound level heard by the person?

2. Relevant equations
maybe:
Doppler
T = 2π √(m/k)

3. The attempt at a solution
a. The highest frequency is when the speaker is the closest to the person. I am thinking using Doppler to find the frequency:
$$f_2=\frac{v±v_o}{v±v_s}f_1$$

But the speed of the speaker is not constant so I don't think Doppler can be used.

The maximum speed is Aω = A√(k/m), but I am stuck...

b. Don't know

2. Oct 20, 2012

### frogjg2003

Well, it's asking for the maximum and minimum frequencies, so you only need the maximum and minimum speeds, which are ±Aω. That's parts a and b.
I'm assuming that sound level refers to the value measured in dB. That means that the sound level is given by $L=20 \log_{10}\left(\frac{p}{p_0}\right)$ which can be rearrange to be L=20log10(p)-β. Here p and p0 are the pressures at the two points. The pressure is inversely proportional to distance, so you can use p0=λ/d and p=λ/(d+Δd) get L as a function of β, d, and Δd. What is Δd?

3. Oct 20, 2012

### songoku

I have never encountered the formula p0=λ/d. λ is the wavelength of the sound wave, and what is d?

4. Oct 20, 2012

### frogjg2003

Oh, i used λ as an arbitrary constant. When you manipulate the math, it will be remove from the equations. d is the distance you were given in the diagram.

5. Oct 20, 2012

### songoku

Actually I still don't really understand the formula and the idea but let me try:
p0=λ/d and p=λ/(d+Δd), where Δd equals to 2A + d

L = 20 log (P/P0)
= 20 log P - 20 log p0
= 20 log λ - 20 log d - 20 log λ + 20 log (2d + 2A)
= 20 log 2 [(d + A)/d]

There is no β term

or

L = 20 log (P/P0)
= 20 log P - 20 log p0
= 20 log λ - 20 log d - β

The term λ does not cancel out

6. Oct 21, 2012

### songoku

I did another work and got answer like this:

$$minimum~sound~level = β + 20 log (\frac{d}{2A+d})$$

7. Oct 21, 2012

### frogjg2003

That looks right.

8. Oct 21, 2012

### songoku

OK thanks a lot for your help