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Exam 14: Mechanical Waves

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Question 1

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A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The stone is heavy enough to prevent the lower end of the wire from moving. What is the mass m of the stone?

A) 8.90 kg
B) 23.1 kg
C) 35.6 kg
D) 227 kg
E) 349 kg

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Question 2

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A 1.0-g string that is 0.64 m long is fixed at both ends and is under tension. This string produces a 100-Hz tone when it vibrates in the third harmonic. The speed of sound in air is 344 m/s. The tension in the string, in is closest to

A) 2.8 N.
B) 2.3 N.
C) 1.8 N.
D) 3.4 N.
E) 3.9 N.

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Question 3

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A guitar string 0.650 m long has a tension of 61.0 N and a mass per unit length of 3.00 g/m. (a) What is the speed of waves on the string when it is plucked? (b) What is the string's fundamental frequency of vibration when plucked?

A platinum wire that is 1.20 m long has a radius of 0.500 mm and is fixed at both ends. In its third harmonic it vibrates at 512 Hz. The density of platinum is 21.4 × 10³ kg/m³. What is the tension in the wire?

A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of the reflected and transmitted pulses?

A tiny vibrating source sends waves uniformly in all directions. An area of 3.25 cm² on a sphere of radius 2.50 m centered on the source receives energy at a rate of 4.20 J/s. (a) What is the intensity of the waves at 2.50 m from the source and at 10.0 m from the source? (b) At what rate is energy leaving the vibrating source of the waves?

A guitar string is fixed at both ends. If you tighten it to increase its tension

Observer A is 3.0 m from a tiny light bulb and observer B is 12.0 m from the same bulb. Assume that the light spreads out uniformly and undergoes no significant reflections or absorption. If observer B sees a light of intensity I, the light intensity that A sees is

Find the speed of an ocean wave whose vertical displacement y as a function of time t is given by y(x,t) = 3.7 cos(2.2x - 5.6t) , where all quantities are in SI units.

For the wave shown in the figure, the wavelength is

The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. Determine the wavelength of the wave.

Four traveling waves are described by the following equations, where all quantities are measured in SI units and y represents the displacement. I: y = 0.12 cos(3x - 21t) II: y = 0.15 sin(6x + 42t) III: y = 0.13 cos(6x + 21t) IV: y = -0.27 sin(3x - 42t) Which of these waves have the same period?

You are generating traveling waves on a stretched string by wiggling one end. If you suddenly begin to wiggle more rapidly without appreciably affecting the tension, you will cause the waves to move down the string

A tube open at one end and closed at the other end produces sound having a fundamental frequency of 350 Hz. If you now open the closed end, the fundamental frequency becomes

A thin taut string is fixed at both ends and stretched along the horizontal x-axis with its left end at x = 0. It is vibrating in its third OVERTONE, and the equation for the vertical displacement of any point on the string is y(x,t) = (1.22 cm) sin[(14.4 m^-1)x] cos[(166 rad/s)t]. (a) What are the frequency and wavelength of the fundamental mode of this string? (b) How long is the string? (c) How fast do waves travel on this string?

Ocean tides are waves that have a period of 12 hours, an amplitude (in some places) of 1.50 m, and a speed of 750 km/hr. What is the distance between adjacent crests of these waves?

Waves travel along a 100-m length of string which has a mass of 55 g and is held taut with a tension of 75 N. What is the speed of the waves?

The density of aluminum is 2700 kg/m3. If transverse waves propagate at 34 m/s in a 4.6-mm diameter aluminum wire, what is the tension on the wire?

A 2.00-m long piano wire with a mass per unit length of 12.0 g/m is under a tension of 8.00 kN. What is the frequency of the fundamental mode of vibration of this wire?

Two violinists are trying to tune their instruments in an orchestra. One is producing the desired frequency of 440.0 Hz. The other is producing a frequency of 448.4 Hz. By what percentage should the out-of-tune musician change the tension in his string to bring his instrument into tune at 440.0 Hz?