Physics for Scientists and Engineers With Modern Physics
9th Edition
ISBN: 9781133953982
Author: SERWAY, Raymond A./
Publisher: Cengage Learning
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Chapter 18, Problem 60P
To determine
Find the first five harmonics of the string A, C#, and E and find the nearest equality of the harmonics of each string.
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A violin string ? = 31.6 cm long and ? = 0.65 g⁄m linear mass density is tuned to play a La4 note at 440.0 Hz. This means that the string is at its fundamental oscillation mode, that is, you will be on that note without placing a finger on it. From this information:
B. If the midpoint of the chord is displaced 1.80 mm transversely when found in the fundamental mode, what is the maximum speed ??á? of the midpoint of string?
When played in a certain manner, the lowest resonant frequency of a certain violin string is concert A (440 Hz).What is the frequency of the (a) second and (b) third harmonic of the string?
A string with a length of 4 m is held under a constant tension. The string has a linear mass density of μ = 0.006 kg/m. Two resonant frequencies of the string are 400 Hz and 480 Hz. There are no resonant frequencies between the two frequencies. (a) What are the wavelengths of the two resonant modes? (b) What is the tension in the string?
Chapter 18 Solutions
Physics for Scientists and Engineers With Modern Physics
Ch. 18.1 - Prob. 18.1QQCh. 18.2 - Consider the waves in Figure 17.8 to be waves on a...Ch. 18.3 - When a standing wave is set up on a string fixed...Ch. 18.5 - Prob. 18.4QQCh. 18.5 - Prob. 18.5QQCh. 18 - Prob. 1OQCh. 18 - Prob. 2OQCh. 18 - Prob. 3OQCh. 18 - Prob. 4OQCh. 18 - Prob. 5OQ
Ch. 18 - Prob. 6OQCh. 18 - Prob. 7OQCh. 18 - Prob. 8OQCh. 18 - Prob. 9OQCh. 18 - Prob. 10OQCh. 18 - Prob. 11OQCh. 18 - Prob. 12OQCh. 18 - Prob. 1CQCh. 18 - Prob. 2CQCh. 18 - Prob. 3CQCh. 18 - Prob. 4CQCh. 18 - Prob. 5CQCh. 18 - Prob. 6CQCh. 18 - Prob. 7CQCh. 18 - Prob. 8CQCh. 18 - Prob. 9CQCh. 18 - Prob. 1PCh. 18 - Prob. 2PCh. 18 - Two waves on one string are described by the wave...Ch. 18 - Prob. 5PCh. 18 - Prob. 6PCh. 18 - Two pulses traveling on the same string are...Ch. 18 - Two identical loudspeakers are placed on a wall...Ch. 18 - Prob. 9PCh. 18 - Why is the following situation impossible? Two...Ch. 18 - Two sinusoidal waves on a string are defined by...Ch. 18 - Prob. 12PCh. 18 - Prob. 13PCh. 18 - Prob. 14PCh. 18 - Prob. 15PCh. 18 - Prob. 16PCh. 18 - Prob. 17PCh. 18 - Prob. 18PCh. 18 - Prob. 19PCh. 18 - Prob. 20PCh. 18 - Prob. 21PCh. 18 - Prob. 22PCh. 18 - Prob. 23PCh. 18 - Prob. 24PCh. 18 - Prob. 25PCh. 18 - A string that is 30.0 cm long and has a mass per...Ch. 18 - Prob. 27PCh. 18 - Prob. 28PCh. 18 - Prob. 29PCh. 18 - Prob. 30PCh. 18 - Prob. 31PCh. 18 - Prob. 32PCh. 18 - Prob. 33PCh. 18 - Prob. 34PCh. 18 - Prob. 35PCh. 18 - Prob. 36PCh. 18 - Prob. 37PCh. 18 - Prob. 38PCh. 18 - Prob. 39PCh. 18 - Prob. 40PCh. 18 - The fundamental frequency of an open organ pipe...Ch. 18 - Prob. 42PCh. 18 - An air column in a glass tube is open at one end...Ch. 18 - Prob. 44PCh. 18 - Prob. 45PCh. 18 - Prob. 46PCh. 18 - Prob. 47PCh. 18 - Prob. 48PCh. 18 - Prob. 49PCh. 18 - Prob. 50PCh. 18 - Prob. 51PCh. 18 - Prob. 52PCh. 18 - Prob. 53PCh. 18 - Prob. 54PCh. 18 - Prob. 55PCh. 18 - Prob. 56PCh. 18 - Prob. 57PCh. 18 - Prob. 58PCh. 18 - Prob. 59PCh. 18 - Prob. 60PCh. 18 - Prob. 61PCh. 18 - Prob. 62APCh. 18 - Prob. 63APCh. 18 - Prob. 64APCh. 18 - Prob. 65APCh. 18 - A 2.00-m-long wire having a mass of 0.100 kg is...Ch. 18 - Prob. 67APCh. 18 - Prob. 68APCh. 18 - Prob. 69APCh. 18 - Review. For the arrangement shown in Figure...Ch. 18 - Prob. 71APCh. 18 - Prob. 72APCh. 18 - Prob. 73APCh. 18 - Prob. 74APCh. 18 - Prob. 75APCh. 18 - Prob. 76APCh. 18 - Prob. 77APCh. 18 - Prob. 78APCh. 18 - Prob. 79APCh. 18 - Prob. 80APCh. 18 - Prob. 81APCh. 18 - Prob. 82APCh. 18 - Prob. 83APCh. 18 - Prob. 84APCh. 18 - Prob. 85APCh. 18 - Prob. 86APCh. 18 - Prob. 87CP
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- The lowest note on a piano (the first harmonic vibration) is the "A" note with frequency 27.5 Hz. A 2.00 m long section of the string has mass 428 grams. The vibrating section of the string is 1.96 m long. The tension required to tune the string properly is The frequency of the tenth harmonic vibration of the string is he wavelength of the tenth harmonic vibration of the string is he wavelength of the tenth harmonic vibration of the string isarrow_forwardA violin string of ?=31.8 cm in length and ?=0.64gm⁄ linear mass density is tuned to play an A4 note at 440.0 Hz. This means that the string is in its fundamental oscillation mode, i.e., it will be on that note without placing any fingers on it. From this information, Calculate the tension on the string that allows it to be kept in tune.arrow_forwardThe A string on a violin has a fundamental frequency of 440 Hz . The length of the vibrating portion is 28 cm , and it has a mass of 0.37 g . Under what tension must the string be placed?Express your answer using two significant figures.arrow_forward
- The C major musical scale has notes C D E F G A B C in order. Select the answers that apply. There are half steps between E and F and between B and C. There are no half steps. The frequencies are uniformly spaced. The scale spans a factor of 2 in frequency. Every note is separated from the one before it by a half step.arrow_forwardA periodic, standing wave exists on a string of length L=2.73m. If a particular wave is measured to have a wave velocity of v=45.86 m/s, what is the frequency (in Hz) of the n=3 vibrational mode?arrow_forwardA steel wire with mass 25.4 g and length 1.30 m is strung on a bass so that the distance from the nut to the bridge is 1.10 m. (a) Compute the linear density of the string._______ kg/m(b) What velocity wave on the string will produce the desired fundamental frequency of the E1 string, 41.2 Hz? ________m/s(c) Calculate the tension required to obtain the proper frequency. ________N(d) Calculate the wavelength of the string's vibration. ________m(e) What is the wavelength of the sound produced in air? (Assume the speed of sound in air is 343 m/s.) _________marrow_forward
- A clarinet is a closed tube, so only odd harmonics are produced in the low register. With all holes covered, the clarinet sounds the note D3 = 146.83 Hz. If all finger holes are kept closed, what would be the next frequency sounded if the clarinet is overblown?arrow_forwardThe fundamental frequency of an open organ pipe corresponds to middle C (261.6 Hz on the chromatic musical scale). The third resonance of a closed organ pipe has the same frequency. What is the length of (a) the open pipe and (b) the closed pipe?arrow_forwardTwo sitar strings A and B playing the note ‘Dha’ are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B is slightly increased and the beat frequency is found to decrease to 3 Hz. What is the original frequency of B if the frequency of A is 427 Hz ?arrow_forward
- You know that certain musical notes sound good together— harmonious—whereas others do not. This harmony is related to the various harmonics of the notes. The musical notes C (262 Hz) and G (392 Hz) make a pleasantsound when played together; we call this consonance. As shown, the harmonics of the two notes are either far from each other or very close to each other (within a few Hz). This is the key to consonance: harmonics that are spaced either far apart or very close. The close harmonics have a beat frequency of a few Hz that is perceived as pleasant. If the harmonics oftwo notes are close but not too close, the rather high beat frequencybetween the two is quite unpleasant. This is what we hear as dissonance.Exactly how much a difference is maximally dissonant is a matter of opinion, but harmonic separations of 30 or 40 Hz seem to be quite unpleasant for most people. Would a G-flat (frequency 370 Hz) and a C played together be consonant or dissonant?A. Consonant B. Dissonantarrow_forwardYou know that certain musical notes sound good together— harmonious—whereas others do not. This harmony is related to the various harmonics of the notes. The musical notes C (262 Hz) and G (392 Hz) make a pleasantsound when played together; we call this consonance. As shown, the harmonics of the two notes are either far from each other or very close to each other (within a few Hz). This is the key to consonance: harmonics that are spaced either far apart or very close. The close harmonics have a beat frequency of a few Hz that is perceived as pleasant. If the harmonics oftwo notes are close but not too close, the rather high beat frequencybetween the two is quite unpleasant. This is what we hear as dissonance.Exactly how much a difference is maximally dissonant is a matter of opinion, but harmonic separations of 30 or 40 Hz seem to be quite unpleasant for most people. An organ pipe open at both ends is tuned so that its fundamental frequency is a G. How long is the pipe?A. 43 cm B.…arrow_forwardYou know that certain musical notes sound good together— harmonious—whereas others do not. This harmony is related to the various harmonics of the notes. The musical notes C (262 Hz) and G (392 Hz) make a pleasantsound when played together; we call this consonance. As shown, the harmonics of the two notes are either far from each other or very close to each other (within a few Hz). This is the key to consonance: harmonics that are spaced either far apart or very close. The close harmonics have a beat frequency of a few Hz that is perceived as pleasant. If the harmonics oftwo notes are close but not too close, the rather high beat frequencybetween the two is quite unpleasant. This is what we hear as dissonance.Exactly how much a difference is maximally dissonant is a matter of opinion, but harmonic separations of 30 or 40 Hz seem to be quite unpleasant for most people. If the C were played on an organ pipe that was open at one end and closed at the other, which of the harmonic…arrow_forward
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