Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Question
Chapter 16, Problem 62P
To determine
The fraction of string by which it must be shortened for given condition.
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The A string on a violin has a fundamental frequency of 430Hz. The length of the vibrating portion of the string is 35cm and has a mass of 0.35 g. Under what tension must the string be placed to obtain the desired frequency?
A 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.
the first violins in the Helium Philharmonic Ochestra all tune their lowest string to a perfect G 196 Hz (this is the fundamental frequency of the string ; it oscillates with no nodes except for the two ends ). If the string is 32 cm long. what is the wavelength of the standing wave ? If the musician plucks the string (pulls it 0.5 cm) near one end , what is the speed of the traveling wave along the string? if the musician plucks it with twice the amplitude (1.0 cm) , what is the speed of the wave ?
Chapter 16 Solutions
Physics for Scientists and Engineers
Ch. 16 - Prob. 1PCh. 16 - Prob. 2PCh. 16 - Prob. 3PCh. 16 - Prob. 4PCh. 16 - Prob. 5PCh. 16 - Prob. 6PCh. 16 - Prob. 7PCh. 16 - Prob. 8PCh. 16 - Prob. 9PCh. 16 - Prob. 10P
Ch. 16 - Prob. 11PCh. 16 - Prob. 12PCh. 16 - Prob. 13PCh. 16 - Prob. 14PCh. 16 - Prob. 15PCh. 16 - Prob. 16PCh. 16 - Prob. 17PCh. 16 - Prob. 18PCh. 16 - Prob. 19PCh. 16 - Prob. 20PCh. 16 - Prob. 21PCh. 16 - Prob. 22PCh. 16 - Prob. 23PCh. 16 - Prob. 24PCh. 16 - Prob. 25PCh. 16 - Prob. 26PCh. 16 - Prob. 27PCh. 16 - Prob. 28PCh. 16 - Prob. 29PCh. 16 - Prob. 30PCh. 16 - Prob. 31PCh. 16 - Prob. 32PCh. 16 - Prob. 33PCh. 16 - Prob. 34PCh. 16 - Prob. 35PCh. 16 - Prob. 36PCh. 16 - Prob. 37PCh. 16 - Prob. 38PCh. 16 - Prob. 39PCh. 16 - Prob. 40PCh. 16 - Prob. 41PCh. 16 - Prob. 42PCh. 16 - Prob. 43PCh. 16 - Prob. 44PCh. 16 - Prob. 45PCh. 16 - Prob. 46PCh. 16 - Prob. 47PCh. 16 - Prob. 48PCh. 16 - Prob. 49PCh. 16 - Prob. 50PCh. 16 - Prob. 51PCh. 16 - Prob. 52PCh. 16 - Prob. 53PCh. 16 - Prob. 54PCh. 16 - Prob. 55PCh. 16 - Prob. 56PCh. 16 - Prob. 57PCh. 16 - Prob. 58PCh. 16 - Prob. 59PCh. 16 - Prob. 60PCh. 16 - Prob. 61PCh. 16 - Prob. 62PCh. 16 - Prob. 63PCh. 16 - Prob. 64PCh. 16 - Prob. 65PCh. 16 - Prob. 66PCh. 16 - Prob. 67PCh. 16 - Prob. 68PCh. 16 - Prob. 69PCh. 16 - Prob. 70PCh. 16 - Prob. 71PCh. 16 - Prob. 72PCh. 16 - Prob. 73PCh. 16 - Prob. 74PCh. 16 - Prob. 75PCh. 16 - Prob. 76PCh. 16 - Prob. 77PCh. 16 - Prob. 78PCh. 16 - Prob. 79PCh. 16 - Prob. 80PCh. 16 - Prob. 81PCh. 16 - Prob. 82PCh. 16 - Prob. 83PCh. 16 - Prob. 84PCh. 16 - Prob. 85PCh. 16 - Prob. 86P
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- A string with a mass of 0.30 kg has a length of 4.00 m. If the tension in the string is 50.00 N, and a sinusoidal wave with an amplitude of 2.00 cm is induced on the string, what must the frequency be for an average power of 100.00 W?arrow_forwardTwo 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_forwardWhat beat frequencies result if a piano hammer hits three strings that emit frequencies of 127.8, 128.1, and 128.3 Hz?arrow_forward
- The speed of a transverse wave on a string is 300.00 m/s, its wavelength is 0.50 m, and the amplitude is 20.00 cm. How much time is required for a particle on the string to move through a distance of 5.00 km?arrow_forwardA 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_forwardA string is fixed at both end. The mass of the string is 0.0090 kg and the length is 3.00 m. The string is under a tension of 200.00 N. The string is driven by a variable frequency source to produce standing waves on the string. Find the wavelengths and frequency of the first four modes of standing waves.arrow_forward
- A string with a mass density mu = 6.40e-03 kg/m is under a tension of F = 259 N and is fixed at both ends. One of its resonance frequencies is 622.0 Hz. The next higher resonance frequency is 777.5 Hz. What is the fundamental frequency of this string? Which harmonic does the resonance frequency at 622.0 Hz correspond to? (i.e. what is n at this frequency?) What is the length of the string? Now, suppose the same string is detached at one end and connected by a ring to a frictionless post, so that it can move freely. Find the wavelength of the first (fundamental) harmonic. What is the frequency of the third (n = 3) harmonic in this case?arrow_forwardThe A string on a violin has a fundamental frequency of 440 Hz . The length of the vibrating portion is 29 cm , and it has a mass of 0.31 g Under what tension must the string be placed? Express your answer using two significant figures.arrow_forwardTwo sitar strings A and B playing the note ‘Ga’ are slightly out of tune and produce beats of frequency 9 Hz. The tension in the string A is slightly reduced and the beat frequency is found to reduce to 6 Hz. If the original frequency of A is 324 Hz, what is the frequency of B?arrow_forward
- A 125 cm length of string has mass 2.00 g and tension 7.00 N. (a) What is the wave speed for this string? (b) What is the lowest resonant frequency of this string?arrow_forward. A piano string is 1.10 m long and has a mass of 9.00 g. (a) How much tension must the string be under if it is to vibrate at a fundamental frequency of 131 Hz? (b) What are the frequencies of the first four harmonicsarrow_forwardWhen a string that is 2m long is connected between two supports and vibrated at 176 Hz it is observed to produce 8 antinodes. If the tension on the string is 77.5 N what would the total mass of the string be?arrow_forward
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