Concept explainers
(a)
The speed of the transverse waves.
(a)
Answer to Problem 76AP
The speed of the transverse waves is
Explanation of Solution
Write the expression for mass per unit length wire.
Here,
Write the expression for tension in the string.
Here,
Conclusion:
Substitute
Substitute
Therefore, the speed of the transverse waves is
(b)
Find the nodes and antinodes distance for three states.
(b)
Answer to Problem 76AP
The simplest pattern for one node and antinode distance is
Explanation of Solution
Since the distance between a node and antinode is one quarter of a wavelength. The string had contained only odd number of node antinode pairs.
Write the expression for simplest pattern AN one node antinode pair.
Here,
Write the expression for simplest pattern ANAN three node antinode pairs.
Here,
Write the expression for simplest pattern ANANAN five node antinode pairs.
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the simplest pattern for one node and antinode distance is
(c)
Find the frequency of nodes and antinodes for three states.
(c)
Answer to Problem 76AP
The frequency of the simplest pattern for one node and antinode distance is
Explanation of Solution
Since the distance between a node and antinode is one quarter of a wavelength. The string had contained only odd number of node antinode pairs.
Write the expression for frequency of the simplest pattern AN one node antinode pair.
Here,
Write the expression for frequency of the simplest pattern ANAN three node antinode pair.
Here,
Write the expression for frequency of the simplest pattern ANANAN five node antinode pair.
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the frequency of the simplest pattern for one node and antinode distance is
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Chapter 18 Solutions
Physics for Scientists and Engineers With Modern Physics
- A nylon siring has mass 5.50 g and length L = 86.0 cm. The lower end is tied to the floor, and the upper end is tied to a small set of wheels through a slot in a track on which the wheels move (Fig. P18.76). The wheels have a mass that is negligible compared with that of the siring, and they roll without friction on the track so that the upper end of the string is essentially free. Figure P18.76 At equilibrium, the string is vertical and motionless. When it is carrying a small-amplilude wave, you may assume the string is always under uniform tension 1.30 N. (a) Find the speed of transverse waves on the siring, (b) The string's vibration possibilities are a set of standing-wave states, each with a node at the fixed bottom end and an antinode at the free top end. Find the node-antinode distances for each of the three simplest states, (c) Find the frequency of each of these states.arrow_forwardA block of mass M is connected to a spring of mass m and oscillates in simple harmonic motion on a frictionless, horizontal track (Fig. P12.69). The force constant of the spring is k, and the equilibrium length is . Assume all portions of the spring oscillate in phase and the velocity of a segment of the spring of length dx is proportional to the distance x from the fixed end; that is, vx = (x/) v. Also, notice that the mass of a segment of the spring is dm = (m/) dx. Find (a) the kinetic energy of the system when the block has a speed v and (b) the period of oscillation. Figure P12.69arrow_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_forward
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- A string has a mass of 150 g and a length of 3.4 m. One end of the string is fixed to a lab stand and the other is attached to a spring with a spring constant of ks = 100 N/m. The free end of the spring is attached to another lab pole. The tension in the string is maintained by the spring. The lab poles are separated by a distance that stretches the spring 2.00 cm. The string is plucked and a pulse travels along the string. What is the propagation speed of the pulse?arrow_forwardA certain string, clamped at both ends, vibrates in seven segments at a frequency of 2.40 × 102 Hz. What frequency will cause it to vibrate in four segments?arrow_forwardA string of 2.74 g and 82 cm in length is attached at one of its ends to one of the arms of a tuning fork with a frequency of 326 Hz that generates electrically operated waves with an energy per unit of time of 24 W. The other end passes through a pulley and supports a mass of 136.5 kg. Use 9.8 m/s2 as the value for the acceleration of gravity. The maximum acceleration of the particles on the string isarrow_forward
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