-8 O Figure 16-32 shows the trans-verse velocity u versus time t of thepoint on a string at x = 0, as a wavepasses through it. The scale on the ver-tical axis is set by u, = 4.0 m/s. Theinkr - uf - d What thes is e(Caution: A calculator does not alwaysgive the proper inverse trig function, socheck your answer by substituting itand an assumed value of o into y(x, 1) and then plotting the function.)Figure 16-32 Problem 8.

The sinusoidal wave equation is,

Answered: -8 O Figure 16-32 shows the trans-…

University Physics Volume 1

18th Edition

ISBN:9781938168277

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

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

Chapter17: Sound

Section: Chapter Questions

Problem 30P: Consider a sound wave moving through the air modeled with the equation...

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Consider the superposition of three wave functions y(x,t)=3.00cmsin(2m1x3s1t) , y(x,t)=3.00cmsin(6m1x+3s1t) , and y(x,t)=3.00cmsin(2m1x4s1t) . What is the height of the resulting wave at position x=3.00 m at time t=10.0 s?
(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.)
Show that the wave equation in one dimension 2fx2=1v22ft2 Is satisfied by any doubly differentiable function of either the form f(x — vt) or f(x + vt).
Energy from the Sun arrives at the top of Earth’s atmosphere with an intensity of 1400 W/m2. How long does it take for 1.80109 J to arrive on an area of 1.00 m2?
Check Your Understanding The wave function above is derived using a sine function. Can a cosine function be used instead?
Check Your Understanding The equations for the wavelengths and the frequencies of the modes of a wave produced on a string: n=2nLn=1,2,3,4,5...andn=nv2L=nf1n=1,2,3,4,5... were derived by considering a wave on a string where there were symmetric boundary conditions of a node at each end. These modes resulted from two sinusoidal waves with identical characteristics except they were moving in opposite directions, confined to a region L with nodes required at both ends.Will the same equations work if there were symmetric boundary conditions with antinodes at each end? What would the normal modes look like for a medium that was free to oscillate on each end? Don’t worry for now if you cannot imagine such a medium, just consider two sinusoidal wave functions in a region of length L, with antinodes on each end.
What is the difference between propagation speed and the frequency of a mechanical wave? Does one or both affect wavelength? If so, how?
Consider a string with under tension with a constant linear mass density. A sinusoidal wave with an angular frequency and amplitude produced by some external driving force. If the frequency of the driving force is decreased to half of the original frequency, how is the timeaveraged power of the wave affected? If the amplitude of the driving force is decreased by half, how is the timeaveraged power affected? Explain your answer.
Consider two sinusoidal sine waves traveling along a string, modeled as y1(x,t)=0.3msin(4m1x+3s1t+3) and y2(x,t)=0.6msin(8m1x6s1t) . What is the height of the resultant wave formed by the interference of the two waves at the position x=1.0 m at time t=3.0 s?
What is the minimum speed at which a source must travel toward you for you to be able to hear that its frequency is Doppler shifted? That is, what speed produces a shift of 0.300% on a day when the speed of sound is 331 m/s?
Consider two sinusoidal waves traveling along a string, modeled as y1(x,t)=0.3msin(4m1x+3s1t) and y2(x,t)=0.6msin(8m1x6s1t) . What is the height of the resultant wave formed by the interference of the two waves at the position x=0.5 m at time t=0.2 s?
Consider a stretched spring, such as a slinky. The stretched spring can support longitudinal waves and transverse waves. How can you produce transverse waves on the spring? How can you produce longitudinal waves on the spring?

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