Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 14, Problem 48P
To determine
The displacement amplitudes of harmonics
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Suppose a flutist plays a 523-Hz C note with first harmonic displacement amplitude A1 = 100 nm. From as shown read, by proportion, the displacement amplitudes of harmonics 2 through 7. Take these as the values A2 through A7 in the Fourier analysis of the sound and assume B1 = B2 = ... = B7 = 0. Construct a graph of the waveform of the sound. Your waveform will not look exactly like the flute waveform as shown because you simplify by ignoring cosine terms; nevertheless, it produces the same sensation to human hearing.
As we said, sound waves can be modeled with sine waves. The standard musical pitch is the
A440 which means that the musical note A4 has a frequency of 440 Hz. So this note oscillates
once every seconds and it could be modeled using the curve y = sin(440- 2nt) = sin(880nt).
For each of the following musical notes, what would w be if we wanted to model the sound
wave with y = sin(wt)?
!!
%3D
(a) (i) C4, (261.63 Hz
(iii) E4, (329.63 Hz)
(v) G4, (392 Hz)
(ii) D4, (293.66 Hz)
(iv) F4, (349.23 Hz)
(vi) B4, (493.88 Hz)
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 in case the value of amplitude A corresponds to the first letter of your name: letter E
A. A=0.1 mB. A=0.15 mC. A=0.2 mÇ. A=0.25 mD. A=0.3 mDh. A=0.35 mE. A=0.4 mË. A=0.45 mF. A=0.5 m
G. A=0.55 mGj. A=0.6 mH. A=0.65 mI. A=0.7 mJ. A=0.75 mK. A=0.8 mL. A=0.85 mLl. A=0.9 mM. A=0.95 m
N. A=1.05 mNj. A= 1.1 mO. A=1.15 mP. A=1.2 mQ. A=1.25 mR. A=1.3 mRr. A=1.35 mS. A=1.4 mSh. A=1.45 m
T. A=1.5 mTh. A=1.55 mU. A=1.6 mV. A=1.65 mX. A=1.7 mXh. A=1.75 mY. A=1.8 mZ. A=1.85 mZh. A=1.9 m
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?…
Chapter 14 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 14.1 - Prob. 14.1QQCh. 14.2 - Prob. 14.2QQCh. 14.3 - When a standing wave is set up on a string fixed...Ch. 14.4 - Prob. 14.4QQCh. 14.4 - Prob. 14.5QQCh. 14.5 - You are tuning a guitar by comparing the sound of...Ch. 14 - A flute has a length of 58.0 cm. If the speed of...Ch. 14 - Prob. 2OQCh. 14 - In Figure OQ14.3, a sound wave of wavelength 0.8 m...Ch. 14 - Prob. 4OQ
Ch. 14 - Prob. 5OQCh. 14 - Prob. 6OQCh. 14 - Prob. 7OQCh. 14 - Prob. 8OQCh. 14 - Prob. 9OQCh. 14 - Prob. 10OQCh. 14 - A standing wave having three nodes is set up in a...Ch. 14 - Prob. 1CQCh. 14 - Prob. 2CQCh. 14 - Prob. 3CQCh. 14 - Prob. 4CQCh. 14 - What limits the amplitude of motion of a real...Ch. 14 - Prob. 6CQCh. 14 - Prob. 7CQCh. 14 - Prob. 8CQCh. 14 - Prob. 1PCh. 14 - Prob. 2PCh. 14 - Prob. 3PCh. 14 - Prob. 4PCh. 14 - Prob. 5PCh. 14 - Prob. 6PCh. 14 - Prob. 7PCh. 14 - Prob. 8PCh. 14 - Prob. 9PCh. 14 - Prob. 10PCh. 14 - Prob. 11PCh. 14 - Prob. 12PCh. 14 - Prob. 13PCh. 14 - Prob. 14PCh. 14 - Prob. 15PCh. 14 - Prob. 16PCh. 14 - Prob. 17PCh. 14 - Prob. 18PCh. 14 - Prob. 19PCh. 14 - Prob. 20PCh. 14 - A string with a mass m = 8.00 g and a length L =...Ch. 14 - Prob. 22PCh. 14 - Prob. 23PCh. 14 - Prob. 24PCh. 14 - Prob. 25PCh. 14 - Review. A sphere of mass M is supported by a...Ch. 14 - Prob. 27PCh. 14 - Prob. 28PCh. 14 - Prob. 29PCh. 14 - Prob. 30PCh. 14 - Prob. 31PCh. 14 - The overall length of a piccolo is 32.0 cm. The...Ch. 14 - Prob. 33PCh. 14 - Prob. 34PCh. 14 - Two adjacent natural frequencies of an organ pipe...Ch. 14 - Do not stick anything into your ear! Estimate the...Ch. 14 - Prob. 37PCh. 14 - As shown in Figure P14.37, water is pumped into a...Ch. 14 - Prob. 39PCh. 14 - Prob. 40PCh. 14 - Prob. 41PCh. 14 - Why is the following situation impossible? A...Ch. 14 - 23. An air column in a glass tube is open at one...Ch. 14 - Prob. 44PCh. 14 - Prob. 45PCh. 14 - Prob. 46PCh. 14 - Prob. 47PCh. 14 - Prob. 48PCh. 14 - Some studies suggest that the upper frequency...Ch. 14 - Prob. 50PCh. 14 - An earthquake can produce a seiche in a lake in...Ch. 14 - Prob. 52PCh. 14 - Prob. 53PCh. 14 - Prob. 54PCh. 14 - Prob. 55PCh. 14 - A nylon string has mass 5.50 g and length L = 86.0...Ch. 14 - Prob. 57PCh. 14 - Prob. 58PCh. 14 - Prob. 59PCh. 14 - Review. For the arrangement shown in Figure...Ch. 14 - Prob. 61PCh. 14 - Prob. 62PCh. 14 - Prob. 63PCh. 14 - Prob. 64PCh. 14 - Prob. 65PCh. 14 - Prob. 66PCh. 14 - Prob. 67PCh. 14 - Review. Consider the apparatus shown in Figure...Ch. 14 - Prob. 69P
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- Item 9 Learning Goal: To learn the properties of logarithms and how to manipulate them when solving sound problems. The intensity of sound is the power of the sound waves divided by the area on which they are incident. Intensity is measured in watts per square meter, or W/m². The human ear can detect a remarkable range of sound intensities. The quietest sound that we can hear has an intensity of 10-12 W/m², and we begin to feel pain when the intensity reaches 1 W/m². Since the intensities matter people in everyday life cover a range of 12 orders of magnitude, intensities are usually converted to a logarithmic scale called the sound intensity level 3, which is measured in decibels (dB). For a given sound intensity I, B is found from the equation ß = (10 dB) log (1), where Io = 1.0 × 10-¹2 W/m². ▼ The logarithm of x, written log(x), tells you the power to which you would raise 10 to get æ. So, if y = log(x), then x = 10³. It is easy to take the logarithm of a number such as 10², because…arrow_forwardA 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…arrow_forwardA 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 value of amplitude A=0.4m. 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…arrow_forward
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