1. A harmonic scalpel is 25 cm long. For a scalpel made of steel, the speed of sound in the material is v = 5800 m/s. The harmonic scalpel can be treated as a column of air open at both ends: I. What would be the fundamental (harmonic) frequency of the standing wave for this device? ll. Draw the rst three harmonic wave patterns (standing waves) for the scalpel. |||. Calculate the frequency of the 3rd harmonic? IV. How many nodes does the 3rd harmonic standing wave have? V. What do nodes and antinodes on the blade represent? What should the tip of the blade be, a node or an antinode? Why? VI. Now assume that the harmonic scalpel is driven at the third harmonic frequency. Assume that the mass of the tip of the scalpel m = 0.05 kg and it is Vibrating at an amplitude of 0.1 mm. Calculate the mechanical energy of the tip. Show the formula. III. Briey explain how the harmonic scalpel can be used to make incisions. An ultrasound wave of frequency 5 MHz and intensity I1 = 1.00 x 10'9 W/m2 at location 1 shown in the gure below travels in tissue of acoustic impedance 1.68 x 106 kg/{s-m2). The half-length of the sound at 5 MHz in tissue is 1.2 cm. The wave travels a distance d and suffers attenuation before reaching the muscle-bone interface at the location 2. 6 pts I. In your words, dene the half-intensity length. ll. Calculate the intensity of sound, l2, after it travels the distance d =2.4 cm equal to two halflengths in tissue and reaches the location 2. III. Location 2 is a muscle bone interface with acoustic impedance of 7.80 x 10'5 kg/(s- m2). Calculate the intensity of the reected beam at 2, Izref. IV. The reected beam now travels back through the tissue and arrives at 1. Calculate the intensity of the reected beam at 1. V. Calculate the percent decrease in intensity in the beam during the round trip. Comment about the percent decrease