L07 & 08

Question 1

Point sources - spherical projector:
1. What does a transducer do?
2. Which waves are emitted?
3. Which quantities are relevant?

Answer 1

1. It transforms El. Energy into mechanical and acoustic field is generated.
2. Spherical waves from a point source, with 2 point sources each interference patterns can be generated.
3. Phi(r,t) =
   phi_0 / r * exp( j( wt- kr + phi_0 ))
   (Derived by solution of spherical wave equation)
4. • p^ (compl. Amp pressure)
   • v^ (c.A. of Particle velocity)
   • q^ = v^ * A (Sound flux!!!!)
   • Zrs = p^ / v^

• P = qrms^2 / A * Re{Zr,s} | spec. Ac. Imp.

P= v~ ^2 * A * Re{Zrs}

q0 =Av = 4piR^2v (2D)

Question 2

What is a property of efficient radiators?

Answer 2

kR&raquo_space;1 (high frequency! But more absorption!)
-> surface wall,
- Re{Zrs} increased!
- Im{Zrs} (moved mass) decreased

Question 3

What is a bad radiator?

Answer 3

kR -> 0 (low frequencies emitted, long wavelengths,
Phi(r) = - q0 / 4pi*r * exp(-jkr)

Question 4

What is the Directivity of a source?
How is it optimized?
What is the directional factor?
How does it affect the Beam pattern?

Answer 4

It is a directional factor generated by the interference pattern of source.

2. Optimization by distancing of sources @ lambda/2 (narrow beam)
   Lambda* 3/2: power distr. In > 2 directions!
   -> power distribution depends on kd!
3. Directional factor H(phi, Theta) <=1
   Determines radiated sound pressure in far field:

Pressure =
axial pressure * directional factor

4. B = 20 log10(H)
   Max B = 0dB

Question 5

What’s the distance between Directivity D and the directional Index?

Answer 5

The Directivity D is a measure, how much Intensity Iax(r) is radiated along the acoustical axis compared to Isphere(r)

Whereas:
The directional factor is on the logarithmic scale 10*log10(D) a measure of the Intensity gain!!!!

Question 6

In which case does the baffled piston have a higher directivity?

Answer 6

When kR is much larger than Lambda,
The interference pattern of radiated pressure does not have nodes anymore.

The less kR the easier the interference pattern.

Directivity is proportional to |kR|^2!!!
The radiation impedance is increased by that factor (|kR|^2) at short kR (-> 10)

Question 7

How do nonlinear effects decrease the emitted power of transducers?

Answer 7

Nonlinear wave equation in space has time derivative of 2nd derivative in space of the pressure more (multipl. with tau),
Which leads to distortion in the pressure radiated over time.
The velocity at the frequency peaks in the spectrum is increased so the distortion at pressure peaks is generated.

Question 8

L08: How is resonance generated?

Question 9

Where is the damping the most?