Question

An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk ( m = 0.13 g ) driven back and forth in SHM at 1.0MHz by an electromagnetic coil.

The maximum restoring force that can be applied to the disk without breaking it is 3.7×10⁴ N . What is the maximum oscillation amplitude that won't rupture the disk?

What is the disk's maximum speed at this amplitude?

Answer 1

m = mass = 0.13 g = 0.13 x 10^-3 kg

f = 10⁶ hz

w = 2pif = 2 x 3.14 x 10⁶ = 6.28 x 10⁶

k = m w² = (0.13 x 10^-3) (6.28 x 10⁶)² = 5.13 x 10⁹

F = 3.7 x 10⁴ N

A = apmlitude

using the formula

F = kA

3.7 x 10⁴ = (5.13 x 10⁹ ) A

A = 7.2 x 10^-6 m

maximum speed is given as

V = Aw = (7.2 x 10^-6 ) (6.28 x 10⁶) = 45.22 m/s