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Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. It's exemplified by the motion of a mass attached to a spring when it's compressed or stretched, and also in the movement of a pendulum. One key characteristic of SHM is that the object oscillates about an equilibrium position and its motion can be described mathematically by sinusoidal functions.

Simple harmonic motion has a fixed frequency, which is the number of oscillations it completes in one second. To completely understand the motion of the fetus's heart wall, which is moving in SHM, we consider its frequency and amplitude, which are 115 cycles per minute and 1.80 mm, respectively. The amplitude refers to the maximum distance from the equilibrium position, while the frequency corresponds to how fast the oscillation occurs. These two parameters are pivotal in characterizing SHM and are essential for calculating other properties such as maximum speed.

The maximum linear speed in simple harmonic motion is a paramount concept as it represents the highest velocity achieved by the oscillating object. In the context of our exercise concerning the fetal heart wall in SHM, the heart wall's maximum linear speed occurs when it passes through the equilibrium position, where all the energy of the system is kinetic.

The formula for calculating the maximum linear speed is given by \( v_{\text{max}} = \omega A \), where \( \omega \) is the angular frequency and \( A \) is the amplitude of motion. Angular frequency is the rate of change of the phase of the sinusoidal waveform, or in other words, it is 2蟺 times the frequency. To find the maximum linear speed, you first need to determine the angular frequency by converting the given frequency into radians per second. The process includes multiplying the frequency by 2蟺 (since one complete cycle is equivalent to 2蟺 radians) and then by the amplitude. Shorter wavelengths and higher frequencies usually imply greater maximum linear speed.

The Doppler effect is an important concept to understand when it comes to waves, such as sound waves. It refers to the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave's source. It can be observed in everyday life, for example, when an ambulance passes with its siren on, the pitch of the siren sounds higher as it approaches and lower as it moves away.

The Doppler effect formula for sound waves is given by \( f' = \frac{f(v + v_{\text{source}})}{v} \) when the wave source is moving towards the observer, and \( f' = \frac{f(v - v_{\text{source}})}{v} \) when it's moving away. In these formulas, \( f' \) is the observed frequency, \( f \) is the emitted frequency, \( v \) is the velocity of waves in the medium, and \( v_{\text{source}} \) is the velocity of the source towards or away from the observer. Knowing the emitted frequency and the maximum linear speed of the heart wall as the wave source, the maximum frequency at which sound arrives at the wall, and the maximum frequency at which the reflected sound is received can be derived.

Ultrasonic frequencies are high-frequency sound waves that are above the human hearing range. They start from approximately 20 kHz and can go into the gigahertz range. In medical applications, ultrasonic waves are frequently used, such as in the fetal heartbeat detectors mentioned in our exercise. To calculate the ultrasonic frequency received due to movement, such as that of a fetal heart wall, one should use the Doppler effect formula adjusted for the specifics of ultrasound.

In this scenario, the original frequency of the emitted ultrasound is 2,000,000.0 Hz, and we use the Doppler effect formula to find the new frequency as sound waves hit and then reflect off the moving heart wall. Since ultrasonic waves travel at a known speed through a medium like body tissue, which in our case is 1.50 km/s, all parameters are set to calculate the accosted ultrasound frequencies that can be detected. The difference between the broadcasted and received frequencies enables the equipment to electronically process and convert these signals into audible sounds, synchronized with the fetal heartbeat.