Please show all steps. Label all variable symbols such as wavelength, wave speed, period etc before using them in a formula. Please write out answer if possible. DO NOT TYPE ANSWERS WITHOUT MULTIPLICATION OR DIVISION SIGNS. 1. Ultrasound is sound waves with frequencies higher than the upper audible limit for humanhearing. Bats use ultrasound to for locating prey and obstacles. Ultrasonic devices are also used todetect objects, measure distances and have many important medical applications. One suchapplication is to monitor fetal heartbeats by reflecting ultrasound waves off the fetus in the womb.In this problem we will explore the ideas of doppler shift and beat frequency to understand howultrasound is used to monitor fetal heart health.UltrasoundtransducerUterus-FetusFetal Ultrasounda.Consider an object moving at speed vo toward an at rest source that is emitting soundwaves of frequency fo. Show that a reflected wave (i.e. the echo) that returns to the source has adoppler shifted frequency offeceno = ) fowhere v is the speed of sound in the medium.b.Rearrange your equation by factoring out the speed of sound in the medium from boththe numerator and the denominator, thus creating two binomials. Using the binomial approximation(or a Taylor expansion), determine an expression for fecho up to first order. The binomialapproximation to first order is given by(1+ x)" z 1+ nxif x « 1.Suppose the objects speed is much less than the wave speed vo « v. When thishappens, the frequency fecho fo. The microphone that is sensitive to these frequencies willdetect a beat frequency if it listens to fecho and fo simultaneously. Use the binomial approximationto show that (up to first order) the beat frequency isfoeat = (2"0/») foThe reflection fecho of the 2.40 MHz ultrasound waves from the surface of a fetus'sbeatıng heart combines with the 2.40 MHz ultrasound waves to produce a beat frequency thatreaches a maximum of 65 Hz. The speed of ultrasound waves within the body is 1540 m/s. What isthe maximum speed of the surface of the fetus's heart? Does your answer seem reasonable?d.Suppose the surface of the heart moves with simple harmonic motion at 90 beats/min.е.What is the amplitude in mm of the heartbeat? Does your answer seem reasonable?

Question

Please show all steps. Label all variable symbols such as wavelength, wave speed, period etc before using them in a formula. Please write out answer if possible. DO NOT TYPE ANSWERS WITHOUT MULTIPLICATION OR DIVISION SIGNS. 1. Ultrasound is sound waves with frequencies higher than the upper audible limit for humanhearing. Bats use ultrasound to for locating prey and obstacles. Ultrasonic devices are also used todetect objects, measure distances and have many important medical applications. One suchapplication is to monitor fetal heartbeats by reflecting ultrasound waves off the fetus in the womb.In this problem we will explore the ideas of doppler shift and beat frequency to understand howultrasound is used to monitor fetal heart health.UltrasoundtransducerUterus-FetusFetal Ultrasounda.Consider an object moving at speed vo toward an at rest source that is emitting soundwaves of frequency fo. Show that a reflected wave (i.e. the echo) that returns to the source has adoppler shifted frequency offeceno = ) fowhere v is the speed of sound in the medium.b.Rearrange your equation by factoring out the speed of sound in the medium from boththe numerator and the denominator, thus creating two binomials. Using the binomial approximation(or a Taylor expansion), determine an expression for fecho up to first order. The binomialapproximation to first order is given by(1+ x)&#34; z 1+ nxif x « 1.Suppose the objects speed is much less than the wave speed vo « v. When thishappens, the frequency fecho fo. The microphone that is sensitive to these frequencies willdetect a beat frequency if it listens to fecho and fo simultaneously. Use the binomial approximationto show that (up to first order) the beat frequency isfoeat = (2&#34;0/») foThe reflection fecho of the 2.40 MHz ultrasound waves from the surface of a fetus'sbeatıng heart combines with the 2.40 MHz ultrasound waves to produce a beat frequency thatreaches a maximum of 65 Hz. The speed of ultrasound waves within the body is 1540 m/s. What isthe maximum speed of the surface of the fetus's heart? Does your answer seem reasonable?d.Suppose the surface of the heart moves with simple harmonic motion at 90 beats/min.е.What is the amplitude in mm of the heartbeat? Does your answer seem reasonable?

Accepted Answer

a)
The frequency of 'f' is given by

Where v is the velocity of sound in the medium.
vs is the…

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