Wave Addition & Phasors Two waves travel in the same direction. They have equal wavelength but unequal amplitude (A₁ < A₂) and interfere. As measured along the axis of travel of the wave ("x"), the resultant wave's crest is: closer to the crest of wave 2 closer to the crest of wave 1 equidistant between the crests of waves 1 & 2 not enough information

Wave Addition & Phasors Two waves travel in the same direction. They have equal wavelength but unequal amplitude (A₁ < A₂) and interfere. As measured along the axis of travel of the wave ("x"), the resultant wave's crest is: closer to the crest of wave 2 closer to the crest of wave 1 equidistant between the crests of waves 1 & 2 not enough information

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter16: Waves

Section: Chapter Questions

Problem 85P: The power versus time for a point on a string (=0.05kg/m) in which a sinusoidal traveling wave is...

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(a) Seismographs measure the arrival times of earthquakes with a precision of 0.100 s. To get the distance to the epicenter of the quake, geologists compare the arrival times of S- and P-waves, which travel at different speeds. If S- and P-waves travel at 4.00 and 7.20 km/s, respectively, in the region considered, how precisely can the distance to the source of the earthquake be determined? (b) Seismic waves from underground detonations of nuclear bombs can be used to locate the test site and detect violations of test bans. Discuss whether your answer to (a) implies a serious limit to such detection. (Note also that the uncertainty is greater if there is an uncertainty in the propagation speeds of the S- and P-waves.)
Check Your Understanding The wave equation 2y(x,t)x2=1v22y(x,t)t2 works for any wave of the form y(x,t)=f(xvt) . In the previous section, we stated that a cosine function could also be used to model a simple harmonic mechanical wave. Check if the wave y(x,t)=0.50mcos(0.20m1x4.00s1t+10) is a solution to the wave equation. Any disturbance that complies with the wave equation can propagate as a wave moving along the x-axis with a wave speed v. It works equally well for waves on a string, sound waves, and electromagnetic waves. This equation is extremely useful. For example, it can be used to show that electromagnetic waves move at the speed of light.
What is the necessary condition on the path length difference between two waves that interfere (a) constructively and (b) destructively?
Consider a sound wave moving through the air modeled with the equation s(x,t)=6.00nmcos(54.93m1x18.84103s1t) . What is the shortest time required for an air molecule to move between 3.00 nm and -3.00 nm?
When two waves interfere constructively or destructively, is there any gain or loss in energy in the system of the waves? Explain.
If you shake the end of a stretched spring up and down with a frequency f, you can produce a sinusoidal, transverse wave propagating down the spring. Does the wave number depend on the frequency you are shaking the spring?
A copper wire has a density of =8920 kg/m3, a radius of 1.20 mm, and a length L. The wire is held under a tension of 10.00 N. Transverse waves are sent down the wire. (a) What is the linear mass density of the wire? (b) What is the speed of the waves through the wire?
Many of the topics discussed in this chapter are useful beyond the topics of mechanical waves. It is hard to conceive of a mechanical wave with sharp corners, but you could encounter such a wave form in your digital electronics class, as shown below. This could be a signal from a device known as an analog to digital converter, in which a continuous voltage signal is converted into a discrete signal or a digital recording of sound. What is the result of the superposition of the two signals?
A sound wave is modeled with the wave function P=1.20Pasin(kx6.28104s1t) and the sound wave travels in air at a speed of v=343.00 m/s. (a) What is the wave number of the sound wave? (b) What is the value for P(3.00 m, 20.00 s)?
Two sinusoidal waves, which are identical except for a phase shift, travel along in the same direction. The wave equation of the resultant wave is yR(x,t)=0.70msin(3.00m1x6.28s1t+/16rad) . What are the angular frequency, wave number, amplitude, and phase shift of the individual waves? .
Check Your Understanding The wave function above is derived using a sine function. Can a cosine function be used instead?
A swimmer in the ocean observes one day that the ocean surface waves are periodic and resemble a sine wave. The swimmer estimates that the vertical distance between the crest and the trough of each wave is approximately 0.45 m, and the distance between each crest is approximately 1.8 m. The swimmer counts that 12 waves pass every two minutes. Determine the simple harmonic wave function that would describes these waves.