Specific Acoustic Impedance of Standing Wave

In summary, to find the specific acoustic impedance for a standing wave, we can divide the complex variable p by the complex term u, using the rule for dividing complex numbers. Simplifying the resulting expression, we get z = P/(rho_sub_0*c), which shows that the specific acoustic impedance is only dependent on the amplitude of the wave and the properties of the medium.
  • #1
ThunderSnow
1
0

Homework Statement


Find the specific acoustic impedance for a standing wave p=Psin(kx)exp(jwt) where p is a complex variable.

Homework Equations


z = p/u (all variables are complex)
u = (A/rho_sub_0*c)*exp^(wt-kx)

The Attempt at a Solution


Approaching this problem it seems that I have all of the equations necessary. However when I divide P/u to find the specific acoustic impedance I get confused on how to handle the complex variables. I canceled the exp(jwt) and the P leaving z=rho_sub_0*c*sin(kx) although I am pretty sure that I broke some rules of complex numbers in that process. Can anyone clarify how to go about handling this division of complex terms. Also is A equivalent in this case to Psin(kx)?
 
Physics news on Phys.org
  • #2


To solve this problem, we can first simplify the expression for u by substituting in the value of A, which is the amplitude of the wave. So, u = (P/rho_sub_0*c)*exp^(wt-kx). Now, we can use the equation for specific acoustic impedance, z = p/u, where p is the complex variable.

To divide complex variables, we can use the rule that the division of two complex numbers is equal to the division of their magnitudes and the difference of their angles. So, in this case, z = (P/u) * (1/exp^(wt-kx)).

Next, we can substitute the value of u into the equation and simplify, z = (P/rho_sub_0*c)*exp^(kx-wt) * (1/exp^(wt-kx)). This simplifies to z = P/(rho_sub_0*c).

So, the specific acoustic impedance for a standing wave p=Psin(kx)exp(jwt) is z = P/(rho_sub_0*c). This means that the specific acoustic impedance is only dependent on the amplitude of the wave and the properties of the medium, represented by rho_sub_0 and c.
 

1. What is specific acoustic impedance of standing wave?

The specific acoustic impedance of a standing wave is a physical quantity that describes the ability of a medium to transmit sound waves. It is defined as the ratio of sound pressure to particle velocity in the medium.

2. How is specific acoustic impedance of standing wave measured?

The specific acoustic impedance of a standing wave can be measured using a device called an impedance tube. This device consists of two chambers separated by a partition, with a microphone and a loudspeaker placed at each end. The ratio of sound pressure and particle velocity at each end can then be used to calculate the specific acoustic impedance.

3. What factors affect the specific acoustic impedance of standing wave?

The specific acoustic impedance of a standing wave is affected by the properties of the medium it is traveling through, such as density and compressibility. It is also influenced by the frequency and amplitude of the sound wave, as well as the geometry of the space in which the wave is standing.

4. Why is the specific acoustic impedance of standing wave important?

The specific acoustic impedance of a standing wave is important because it helps us understand and predict how sound waves will behave in different mediums. It is also used in the design and analysis of acoustic systems, such as acoustic insulation or soundproofing materials.

5. How does the specific acoustic impedance of standing wave relate to the speed of sound?

The specific acoustic impedance of a standing wave is directly related to the speed of sound in a medium. In fact, the product of specific acoustic impedance and density of the medium is equal to the speed of sound. This means that as the specific acoustic impedance increases, the speed of sound also increases, and vice versa.

Similar threads

  • Advanced Physics Homework Help
Replies
2
Views
996
Replies
1
Views
484
Replies
7
Views
2K
Replies
7
Views
1K
  • Advanced Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
943
  • Special and General Relativity
Replies
16
Views
877
  • Advanced Physics Homework Help
Replies
9
Views
4K
  • Advanced Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
2K
Back
Top