Exam 11: Oscillations and Waves

A 0.250-kg stone is attached to an ideal spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the force constant (spring constant) of the spring?

A 0.50-kg box is attached to an ideal spring of force constant (spring constant) 20 N/m on a horizontal, frictionless floor. The box oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. (a) What is the amplitude of vibration? (b) At what distance from the equilibrium position are the kinetic energy and the potential energy the same?

Which one of the curves shown in the figure best represents the variation of wave speed v as a function of tension for transverse waves on a stretched string?

The position of an object that is oscillating on an ideal spring is given by x=(17.4 cm) Write an expression for the acceleration of the particle as a function of time using the cosine function.

A 4.0-g string is 0.36 m long and is under tension. The string vibrates at 500 Hz in its third harmonic. What is the wavelength of the standing wave in the string?

A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. What are the (a) maximum speed and (b) maximum acceleration of the tip of the needle?

The position of an object that is oscillating on a spring is given by the equation x = (18.3 cm) cos[(2.35 s-1)t]. What are the (a) frequency, (b) amplitude, and (c) period of this motion?

A ball is attached to an ideal spring and oscillates with a period T. If the mass of the ball is doubled, what is the new period?

The average intensity of sunlight impinging on Earth is measured to be about $1.4 \mathrm {~kW} / \mathrm { m } ^ { 2 }$ What is the power of sunlight emitted by the sun? $\text { (Earth-Sun distance } = 1.5 \times 10 ^ { 8 } \mathrm {~km} \text {, Earth radius } = 6.4 \times$ $\left. 10 ^ { 3 } \mathrm {~km} \right)$

A wave whose wavelength is 0.500 m is traveling down a 500-m long wire whose total mass is 25 kg and is under a tension of 2000 N. (a) What is the speed of the wave on the wire? (b) Find the frequency of this wave.

The quartz crystal in a digital watch has a frequency of 32.8 kHz. What is its period of oscillation?

When a 0.350-kg package is attached to a vertical spring and lowered slowly, the spring stretches 12.0 cm. The package is now displaced from its equilibrium position and undergoes simple harmonic oscillations when released. What is the period of the oscillations?

A simple pendulum has a period T on Earth. If it were used on Planet X, where the acceleration due to gravity is 3 times what it is on Earth, what would its period be?

Light from a laser forms a 1.31-mm diameter spot on a wall. If the light intensity in the spot is $1.58 \times 10 ^ { 4 } \mathrm {~W} / \mathrm { m } ^ { 2 }$ what is the power output of the laser? Assume that all the light emitted by the Iaser hits the spot.

Standing waves of frequency 17 Hz are produced on a string that has a mass per unit length of 0.0160 kg/m. To what tension must the string be stretched between two supports if adjacent nodes in the standing wave are to be 0.87 m apart?

A sewing machine needle moves in simple harmonic motion with a frequency of 2.5 Hz and an amplitude of 1.27 cm. (a) How long does it take the tip of the needle to move from the highest point to the lowest point in its travel? (b) How long does it take the needle tip to travel a total distance of 11.43 cm?

The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the velocity of this system as a Function of time?

A simple harmonic oscillator oscillates with frequency f when its amplitude is A. If the amplitude is now doubled to 2A, what is the new frequency?

An object oscillates such that its position x as a function of time t obeys the equation where t is in seconds. (a) In one period, what total distance does the object move? (b) What is the frequency of the motion? (c) What is the position of the object when t=1.00 s?

Four waves are described by the following equations, where distances are measured in meters and times in seconds. Which of these waves have the same speed?