Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 16, Problem 21P
To determine
The explanation to tune a piano string to a tuning fork of known frequency.
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what is the angular frequency ω of the third harmonic in a pipe that is 1.5 m long with one closed end?
A violin string L = 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:
When playing the violin, different notes may be produced depending on the position of the the fingers of one hand on the string. The usual technique forcefully presses the string against the fingerboard, reducing the length of the string that can vibrate. If we consider this string initially tuned for a La4 note, and a finger is placed one third of the length, down from headstock:
i. What would be the frequency of the new note being produced assuming a tension of 50,26N?
A violin string L = 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:
When playing the violin, different notes may be produced depending on the position of the the fingers of one hand on the string. The usual technique forcefully presses the string against the fingerboard, reducing the length of the string that can vibrate. If we consider this string initially tuned for a La4 note, and a finger is placed one third of the length, down from headstock:
i. What would be the frequency of the new note being produced assuming a tension of 50,26N ?
ii. What would the new frequency be, if instead of using the described technique previously to play the violin, the technique called harmonic is used, where the string is only partially depressed so that a node is produced on the string in that position,…
Chapter 16 Solutions
Physics for Scientists and Engineers
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- A string has a linear mass density µ, a length L, and a tension of FT, and oscillates in a mode n at a frequency f. Find the ratio of ff for a small change in tension.arrow_forwardReview. For the arrangement shown in Figure P14.60, the inclined plane and the small pulley are frictionless; the string supports the object of mass M at the bottom of the plane; and the string has mass m. The system is in equilibrium, and the vertical part of the string has a length h. We wish to study standing waves set up in the vertical section of the string. (a) What analysis model describes the object of mass M? (b) What analysis model describes the waves on the vertical part of the string? (c) Find the tension in the string. (d) Model the shape of the string as one leg and the hypotenuse of a right triangle. Find the whole length of the string. (e) Find the mass per unit length of the string. (f) Find the speed of waves on the string. (g) Find the lowest frequency for a standing wave on the vertical section of the string. (h) Evaluate this result for M = 1.50 kg, m = 0.750 g, h = 0.500 m, and θ = 30.0°. (i) Find the numerical value for the lowest frequency for a standing wave on the sloped section of the string. Figure P14.60arrow_forwardYou are given two wind instruments of identical length. One is open at both ends, whereas the other is closed at one end. Which is able to produce the lowest frequency?arrow_forward
- Review. An aluminum wire is held between two clamps under zero tension at room temperature. Reducing the temperature, which results in a decrease in the wires equilibrium length, increases the tension in the wire. Taking the cross-sectional area of the wire to be 5.00 10-6 m2, the density to be 2.70 103 kg/m3, and Young's modulus to be 7.00 1010 N/m2, what strain (L/L.) results in a transverse wave speed of 100 m/s?arrow_forwardA harmonic transverse wave function is given by y(x, t) = (0.850 m) sin (15.3x + 10.4t) where all values are in the appropriate SI units. a. What are the propagation speed and direction of the waves travel? b. What are the waves period and wavelength? c. What is the amplitude? d. If the amplitude is doubled, what happens to the speed of the wave?arrow_forwardA wave is modeled with the function y(x,t)=(0.25m)cos(0.30m1x0.90s1t+3) . Find the (a) amplitude, (b) wave number, (c) angular frequency, (d) wave speed, (e) phase shift, (f) wavelength, and (g) period of the wave.arrow_forward
- A string with a linear mass density of 0.0075 kg/m and a length of 6.00 m is set into the n=4 mode of resonance by driving with a frequency of 100.00 Hz. What is the tension in the string?arrow_forwardA nylon guitar string is fixed between two lab posts 2.00 m apart. The string has a linear mass density of =7.20 g/m and is placed under a tension of 160.00 N. The string is placed next to a tube, open at both ends, of length L. The string is plucked and the tube resonates at the n=3 mode. The speed of sound is 343 m/s. What is the length of the tube?arrow_forwardWhen a tuning fork is held over the open end of a very thin tube, as in the figure, the smallest value of L that produces resonance is found to be 25.5 cm. What is the next larger value of L that will produce resonance with the same tuning fork?arrow_forward
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