Finding displacement amplitude given frequency and pressure

In summary, displacement amplitude is the maximum distance a particle or object moves from its equilibrium position when subjected to a vibration or wave. It is directly proportional to pressure and inversely proportional to frequency. While it cannot be measured directly, it can be calculated using other measurements or indirect methods. The units used to measure displacement amplitude are typically meters, millimeters, micrometers, nanometers, or inches. It also has a direct impact on the intensity of a wave, with a higher displacement amplitude resulting in a stronger and more forceful sound or vibration.
  • #1
leinad0213
8
0

Homework Statement



What is the displacement amplitude of a sound wave of frequency 160.0 Hz in air at 20 °C at the pain-threshold pressure amplitude of 29.0 Pa?

f = 160 Hz
Vs = 343 m/s
ΔP = 29 Pa

Homework Equations



ΔP(x,t) = (ΔP)cos(kx - wt) = β*s*k*cos(kx - wt)
k = f/Vs

The Attempt at a Solution



ΔP = βsk

Therefore, s = ΔP/(β*k) = (ΔP*Vs)/(f*β)

β = 1.4 * 10^5 Pa

So the answer I got was 4.44*10^-4 m which is wrong. Am I missing something here?
 
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  • #2
k=f/Vs is not accurate, since k is 2π/λ

λf = Vs

ω/k = Vs
 

1. What is displacement amplitude?

Displacement amplitude is the maximum distance a particle or object moves from its equilibrium position when subjected to a vibration or wave.

2. How is displacement amplitude related to frequency and pressure?

The displacement amplitude is directly proportional to the pressure and inversely proportional to the frequency of the wave. This means that as the pressure increases or the frequency decreases, the displacement amplitude also increases.

3. Can displacement amplitude be measured directly?

Displacement amplitude cannot be measured directly, but it can be calculated using other measurements such as pressure and frequency. Different methods, such as laser interferometry, can also be used to indirectly measure displacement amplitude.

4. What units are used to measure displacement amplitude?

Displacement amplitude is typically measured in meters (m) or its decimal multiples such as millimeters (mm) or micrometers (µm). In some cases, it may also be measured in other units such as nanometers (nm) or inches (in).

5. How does displacement amplitude affect the intensity of a wave?

The displacement amplitude is directly related to the intensity of a wave. As the displacement amplitude increases, the intensity of the wave also increases, resulting in a louder or more forceful sound or vibration.

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