Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Textbook Question
Chapter 14, Problem 69P
Show by differentiation and substitution that a wave described by Equation 14.3 satisfies the wave equation (Equation 14.5), with wave speed v = ω/k.
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A standing wave is the result of superposition of two harmonic waves given by the equations y1(x;t) =Asin(ωt - kx) and y2(x; t) = Asin(ωt + kx). The angular frequency is ω = 3π rad/s and the k = 2πrad/m is the wave number.(a) Give an expression for the amplitude of standing wave.
A standing wave is the result of superposition of two harmonic waves given by the equations y1(x;t) =Asin(ωt - kx) and y2(x; t) = Asin(ωt + kx). The angular frequency is ω = 3π rad/s and the k = 2πrad/m is the wave number.(a) Give an expression for the amplitude of standing wave.
b) calculate the frequency of the wave
A wave is modeled by the wave function:
y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)]
1. Find the wavelength, wave number, wave velocity, period and wave frequency.
2. Construct on the computer, in the same graph, the dependence of y (x, t) from x on t = 0 and t = 5 s and the amplitude is A= 1.3m
3. After constructing the graph, make the appropriate interpretations and comments from the result that you got graphically.
4. How much is the wave displaced during the time interval from t = 0 to t = 5 s? Does it match this with the graph results? Justify your answer. Is the material transported long wave displacement? If yes, how much material is transported over time interval from t = 0 to t = 5 s? Comment on your answer. We now consider two sound waves with different frequencies which have to the same amplitude. The wave functions of these waves are as follows:
y1 (t) = A sin (2πf1t)
y2 (t) = A sin (2πf2t)
5. Find the resultant wave function analytically.
6. Study how the resulting wave…
Chapter 14 Solutions
Essential University Physics (3rd Edition)
Ch. 14.1 - A boat bobs up and down on a water wave, moving 2...Ch. 14.2 - The figure shows snapshots of two waves...Ch. 14.3 - Two identical stars are different distances from...Ch. 14.4 - Your band needs a new guitar amplifier, and the...Ch. 14.5 - Light shines through two small holes into a dark...Ch. 14.6 - Youre holding one end of a taut rope, and you cant...Ch. 14.7 - A string 1 m long is clamped tightly at one end...Ch. 14.8 - In Fig. 14.35, which is moving faster in relation...Ch. 14 - What distinguishes a wave from an oscillation?Ch. 14 - Red light has a longer wavelength than blue light....
Ch. 14 - Prob. 3FTDCh. 14 - As a wave propagates on a string, the string moves...Ch. 14 - If you doubled the tension in a string, what would...Ch. 14 - A heavy cable is hanging vertically, its bottom...Ch. 14 - Prob. 7FTDCh. 14 - Medical ultrasound uses frequencies around 107 Hz,...Ch. 14 - If you double the pressure of a gas while keeping...Ch. 14 - Water is about a thousand times more dense than...Ch. 14 - Prob. 11FTDCh. 14 - When a wave source moves relative to the medium, a...Ch. 14 - Why can a boat easily produce a shock wave on the...Ch. 14 - Ocean waves with 18-m wavelength travel at 5.3...Ch. 14 - Prob. 15ECh. 14 - Prob. 16ECh. 14 - Prob. 17ECh. 14 - A seismograph located 1250 km from an earthquake...Ch. 14 - Medical ultrasound waves travel at about 1500 m/s...Ch. 14 - An ocean wave has period 4.1 s and wavelength 10.8...Ch. 14 - Find the (a) amplitude, (b) wavelength, (c)...Ch. 14 - Ultrasound used in a medical imager has frequency...Ch. 14 - Prob. 23ECh. 14 - Prob. 24ECh. 14 - Prob. 25ECh. 14 - A transverse wave 1.2 cm in amplitude propagates...Ch. 14 - A transverse wave with 3.0-cm amplitude and 75-cm...Ch. 14 - Prob. 28ECh. 14 - Prob. 29ECh. 14 - Show that P/ from Equation 14.9 has the units of...Ch. 14 - Find the sound speed in air under standard...Ch. 14 - Timers in sprint races start their watches when...Ch. 14 - The factor for nitrogen dioxide (NO2) is 1.29....Ch. 14 - A gas with density 1.0 kg/m3 and pressure 81 kN/m2...Ch. 14 - Prob. 35ECh. 14 - Youre flying in a twin-engine turboprop aircraft,...Ch. 14 - Prob. 37ECh. 14 - A 2.0-m-long string is clamped at both ends. (a)...Ch. 14 - When a stretched string is clamped at both ends,...Ch. 14 - A string is clamped at both ends and tensioned...Ch. 14 - A crude model of the human vocal tract treats it...Ch. 14 - A car horn emits 380-Hz sound. If the car moves at...Ch. 14 - A fire stations siren is blaring at 85 Hz. Whats...Ch. 14 - A fire trucks siren at rest wails at 1400 Hz;...Ch. 14 - Red light emitted by hydrogen atoms at rest in the...Ch. 14 - Figure 14.36 shows a simple harmonic wave at time...Ch. 14 - Prob. 47PCh. 14 - Prob. 48PCh. 14 - Figure 14.37 shows a wave train consisting of two...Ch. 14 - A loudspeaker emits energy at the rate of 50 W,...Ch. 14 - Prob. 51PCh. 14 - Prob. 52PCh. 14 - Prob. 53PCh. 14 - A wire is under 32.8-N tension, carrying a wave...Ch. 14 - A spring of mass m and spring constant k has an...Ch. 14 - Prob. 56PCh. 14 - Prob. 57PCh. 14 - Figure 14.38 shows two observers 20 m apart on a...Ch. 14 - An ideal spring is stretched to a total length L1....Ch. 14 - Prob. 60PCh. 14 - You see an airplane 5.2 km straight overhead....Ch. 14 - What are the intensities in W/m2 of sound with...Ch. 14 - Show that a doubling of sound intensity...Ch. 14 - Sound intensity from a localized source decreases...Ch. 14 - At 2.0 in from a localized sound source you...Ch. 14 - The A-string (440 Hz) on a piano is 38.9 cm long...Ch. 14 - Prob. 67PCh. 14 - Youre designing an organ for a new concert hall;...Ch. 14 - Show by differentiation and substitution that a...Ch. 14 - Prob. 70PCh. 14 - Youre a marine biologist concerned with the effect...Ch. 14 - A 2.25-m-long pipe has one end open. Among its...Ch. 14 - Prob. 73PCh. 14 - Obstetricians use ultrasound to monitor fetal...Ch. 14 - Prob. 75PCh. 14 - You move at speed u toward a wave source thats...Ch. 14 - Youre a meteorologist specifying a new Doppler...Ch. 14 - Use a computer to form the sum implied in the...Ch. 14 - Your little sister and her friend build treehouses...Ch. 14 - An airport neighborhood is concerned about the...Ch. 14 - Tsunamis are ocean waves generally produced when...Ch. 14 - Tsunamis are ocean waves generally produced when...Ch. 14 - Tsunamis are ocean waves generally produced when...Ch. 14 - Tsunamis are ocean waves generally produced when...
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