Question

An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk ( m = 0.14g ) driven back and forth in SHM at 1.0MHz by an electromagnetic coil.

Part A: The maximum restoring force that can be applied to the disk without breaking it is 3.9

Answer 1

A = 3.9x10^4/(4*pi^2*1.4x10^-4*10^12) = 7.056x10^-6 = 7.056 microns

V = 2pi*10^6*7.056x10^-6 = 44.336 m/s

Answer 2

Since, F =-kx
x = - F/k
k = m.?2 = m.4.?²f²
= 0.14 x10^-3 x 4 x 3.14x 3.14 x10⁶x10⁶
= 5.52 *10⁹
(A) Amplitude
A = x = F/k = 3.9*10⁴/5.52x10⁹ = 7.06 x 10^-6 m

(B) Max speed
v_m = ?.A = 2?.f.A
= 2*3.14*10⁶ * 7.06*10^-6
= 44.37 m/s

Answer 3

Since, F =-kx
x max = F/k
k =m.?2 = m.4.?2f2
=0.14x10^-3 x4x3.14x3.14x10^6x10^6
= 5.527x10^9
Amplitude,
A = x max = F/k = 39000/5.527x10^9
= 7.05x 10^-6m =5.79 micrometers
Max speed,
vmax = ?.A = 2?.f.A
= 6.282 x10^6x7.05x10^-6
= 44.28m/s