Concept explainers
(a)
Rank the functions from largest to the smallest according to their amplitude.
(a)
Answer to Problem 3OQ
The ranking of functions from largest to the smallest according to their amplitude is
Explanation of Solution
Write the general expression for a sinusoidal wave.
Here,
Consider wave function (a).
Compare equation (I) and (II). The amplitude of the wave (a) is
Consider wave function (b).
Compare equation (I) and (III). The amplitude of the wave (b) is
Consider wave function (c).
Compare equation (I) and (IV). The amplitude of the wave (c) is
Consider wave function (d).
Compare equation (I) and (V). The amplitude of the wave (d) is
Consider wave function (e).
Compare equation (I) and (VI). The amplitude of the wave (e) is
Thus the raking of amplitude each wave from largest to the smallest is (c)=(d)>(e)>(b)>(a).
Conclusion:
Therefore, the ranking of wave functions from largest to the smallest according to their amplitude is
(b)
Rank the functions from largest to the smallest according to their wavelength.
(b)
Answer to Problem 3OQ
The ranking of functions from largest to the smallest according to their wavelength is
Explanation of Solution
Write the expression for wavelength.
Conclusion:
Substitute,
Substitute,
Substitute,
Substitute,
Substitute,
Thus, the ranking of wavelength from larger to smaller is (c)>(a)=(b)>(d)>(e).
Therefore, the ranking of functions from largest to the smallest according to their wavelength is
(c)
Rank the functions from largest to the smallest according to their frequencies.
(c)
Answer to Problem 3OQ
The ranking of functions from largest to the smallest according to their frequency is
Explanation of Solution
Write the expression for frequency.
Conclusion:
Substitute,
Substitute,
Substitute,
Substitute,
Substitute,
Thus, the ranking of frequencies of wave from largest to smallest is (e)>(d)>(a)=(b)=(c).
Therefore, the ranking of functions from largest to the smallest according to their frequency is
(d)
Rank the functions from largest to the smallest according to their period.
(d)
Answer to Problem 3OQ
The ranking of functions from largest to the smallest according to their period is
Explanation of Solution
Write the expression for period.
Conclusion:
Since frequency is inversely proportional to time period, the ranking will be the reverse order of the ranking in part (c).
Thus, the ranking of functions from largest to the smallest according to their period is
Therefore, the ranking of functions from largest to the smallest according to their period is
(e)
Rank the functions from largest to the smallest according to their speed.
(e)
Answer to Problem 3OQ
The ranking of functions from largest to the smallest according to their speed is
Explanation of Solution
Write the expression for speed.
Conclusion:
Substitute,
Substitute,
Substitute,
Substitute,
Substitute,
Thus, the ranking of speed of the wave from largest to smallest is (c)>(a)=(b)=(d)>(e).
Therefore, ranking of functions from largest to the smallest according to their speed is
Want to see more full solutions like this?
Chapter 16 Solutions
Physics: for Science.. With Modern. -Update (Looseleaf)
- A sound wave in air has a pressure amplitude equal to 4.00 103 Pa. Calculate the displacement amplitude of the wave at a frequency of 10.0 kHz.arrow_forwardThe equation of a harmonic wave propagating along a stretched string is represented by y(x, t) = 4.0 sin (1.5x 45t), where x and y are in meters and the time t is in seconds. a. In what direction is the wave propagating? be. N What are the b. amplitude, c. wavelength, d. frequency, and e. propagation speed of the wave?arrow_forwardA taut rope has a mass of 0.180 kg and a length of 3.60 m. What power must be supplied to the rope so as to generate sinusoidal waves having an amplitude of 0.100 m and a wavelength of 0.500 m and traveling with a speed of 30.0 m/s?arrow_forward
- Two sinusoidal waves are moving through a medium in the same direction, both having amplitudes of 3.00 cm, a wavelength of 5.20 m, and a period of 6.52 s, but one has a phase shift of an angle . What is the phase shift if the resultant wave has an amplitude of 5.00 cm? [Hint: Use the trig identity sinu+sinv=2sin(u+v2)cos(uv2)arrow_forwardA cable with a linear density of =0.2 kg/m is hung from telephone poles. The tension in the cable is 500.00 N. The distance between poles is 20 meters. The wind blows across the line, causing the cable resonate. A standing waves pattern is produced that has 4.5 wavelengths between the two poles. The air temperature is T=20C . What are the frequency and wavelength of the hum?arrow_forwardAt t = 0, a transverse pulse in a wire is described by the function y=6.00x2+3.00 where xand y are in meters. If the pulse is traveling in the positive x direction with a speed of 4.50 m/s, write the function y(x, t) that describes this pulse.arrow_forward
- When a standing wave is set up on a string fixed at both ends, which of the following statements is true? (a) The number of nodes is equal to the number of antinodes. (b) The wavelength is equal to the length of the string divided by an integer. (c) The frequency is equal to the number of nodes times the fundamental frequency. (d) The shape of the string at any instant shows a symmetry about the midpoint of the string.arrow_forwardThe overall length of a piccolo is 32.0 cm. The resonating air column is open at both ends. (a) Find the frequency of the lowest note a piccolo can sound. (b) Opening holes in the side of a piccolo effectively shortens the length of the resonant column. Assume the highest note a piccolo can sound is 4 000 Hz. Find the distance between adjacent anti-nodes for this mode of vibration.arrow_forwardIn Figure OQ14.3, a sound wave of wavelength 0.8 m divides into two equal parts that recombine to interfere constructively, with the original difference between their path lengths being |r2 − r1| = 0.8 m. Rank the following situations according to the intensity of sound at the receiver from the highest to the lowest. Assume the tube walls absorb no sound energy. Give equal ranks to situations in which the intensity is equal. (a) From its original position, the sliding section is moved out by 0.1 m. (b) Next it slides out an additional 0.1 m. (c) It slides out still another 0.1 m. (d) It slides out 0.1 m more. Figure OQ14.3arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning