Physics 112-4 Fall 2011 p1 Homework assignment #1: Chapter 14 Page #243: #1: What distinguishes a wave from an oscillation? #5: Must a wave be either transverse or longitudinal? Explain. #9: The intensity of light from a localized source decreases as the inverse square of the distance from the source. Does this mean that the light loses energy as it propagates? #11: If you double the pressure of a gas while keeping its density the same, what happens to the sound speed? #13: Why can a boat easily produce a shock wave on the water surface, while only a very high-speed aircraft can produce a sonic boom? #16: Ocean waves with 18m wavelength travel at 34 cm/s. What’s the time interval between wave crests passing a boat moored at a fixed location? #21: Medical ultrasound waves travel at about 1500 m/s in soft tissue. High frequencies provide clearer images but don’t penetrate to deeper organs. Find the wavelengths of (a) 8.0 MHz ultrasound used in fetal imaging, and (b) 3.5 MHz ultrasound used to image an adult’s kidneys. #26: Analysis of waves in shallow water (depth much less than wave-length) yields the following wave equation: 𝜕2𝑦 1 𝜕2𝑦 = 𝜕𝑥 2 𝑔ℎ 𝜕𝑡 2 Where h is the water depth and g is the gravitational acceleration. Give an expression for the wave speed. 𝛾𝑃 #32: Show that the quantity √𝑃⁄𝜌 from the equation 𝑣 = √ 𝜌 (equation 14.9) has the units of speed. #33 Find the speed of sound in air under standard conditions with pressure 101 kN/m2 and density 1.20 kg/m3. Page 244: #38: You’re in an airplane whose two engines are running at 560rpm and 570 rpm. How often do you hear a peak in the sound intensity? Physics 112-4 Fall 2011 p2 #40: A 2-m-long string is clamped at both ends. (a) Find the longest wavelength standing wave possible on this string. (b) If the wave speed is 46 m/s, what is the lowest standing-wave frequency? #43: A crude model of the human vocal tract treats it as a pipe closed at one end. Find the effective length of the vocal tract in a person whose fundamental tone is 620Hz. Sound speed in air at body temperature is 354 m/s. #47: Red light emitted by hydrogen atoms at rest in the laboratory has wavelength 656nm. Light emitted in the same process on a distant galaxy is received at Earth with wavelength 708 nm. Describe the galaxy’s motion relative to earth. #49: Transverse waves propagate at 18 m/s on a string under 14N tension. What will be the wave speed if the tension is increased to 40N? #52: A loudspeaker emits energy at the rate of 50W, spread in all directions. Find the intensity of sound 18m from the speaker. #68: The A-String (440Hz) on a piano is 38.9cm long and is clamped tightly at both ends. If the string is under 667N tension, what’s its mass? Page 245: #73. You’re standing roadside as a truck approaches, and you measure the dominant frequency in the truck noise to be 1100Hz. As the truck passes, the frequency drops to 950Hz. What’s the truck’s speed? #78: Obstetricians used ultrasound to monitor fetal heartbeat. If a 5.0 MHz ultrasound reflects off the moving heart wall with a 100Hz shift in frequency, what’s the speed of the heart wall? (Hint: You have two shifts to consider.) #81: You’re a meteorologist specifying a new Doppler system that determines the velocity of distant raindrops by reflecting radar signals (which travel at the speed of light) off them and measuring Doppler shift. You need a system that will measure speeds as low as 2.5 km/h. A vendor offers a 5.0GHz radar that can detect a shift of only 50Hz. Is that sufficient?