Exam 11: Oscillations and Waves

When a certain simple pendulum is set swinging, its angular displacement as a function of time t obeys the equation How long is the pendulum?

If a guitar string has a fundamental frequency of 500 Hz, which one of the following frequencies can set the string into resonant vibration?

A 92-kg man climbs into a car with worn out shock absorbers, and this causes the car to drop down 4.5 cm. As he drives along he hits a bump, which starts the car oscillating at an angular frequency of 4.52 rad/s. What is the mass of the car?

What is the wavelength of the wave shown in the figure?

A spaceship captain lands on an unknown planet. Before venturing forth, he needs to find out the acceleration due to gravity on that planet. All he has available to him is some thin light string, a stopwatch, and a small 2.75-kg metal ball (it was a rough landing). So he lets the ball swing from a 1.5-m length of the string, starting at rest, and measures that it takes 1.9 s for it to swing from the place where he released it to the place where it first stops as it reverses direction. What is the acceleration due to gravity on this planet?

A guitar-like stringed instrument has a string that is 16 cm long. It sounds the musical note A(440 Hz) when played without fingering. By what distance should you shorten it to play the note C (523 Hz)?

A guitar string 0.65 m long has a tension of 61 N and a mass per unit length of 3.0 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? (c) At what other frequencies will this string vibrate?

The figure shows a "snapshot" of a wave at a given instant of time. The frequency of this wave is 120 Hz. What are the (a) amplitude, (b) wavelength, and (c) speed of this wave?

A rope with a total mass of 25.0 kg is tied to a tree on one side of a 125-m wide ravine. You are pulling on the other end of the rope with a force of 415 N. If you pluck the rope at your end, how long will it take the pulse to travel across the ravine to the tree?

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 period?

A 0.50-kg object is attached to an ideal spring of spring constant (force constant) 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What are (a) the total energy and (b) the amplitude of vibration of the system?

A 0.30-kg block of wood is suspended on a spring. In equilibrium the wood stretches the spring 2.0 cm downward. The wood is then pulled an additional distance of 1.0 cm down and released from rest. (a) How long does it take the wood to make 3 complete cycles of vibration? (b) How much total mechanical energy does this system contain if we choose the total potential energy (elastic and gravitational) to be zero at the equilibrium position of the hanging block?

An object is oscillating on a spring with a period of 4.60 s. At time t=0.00 s the object has zero speed and is at x=8.30 cm. What is the acceleration of the object at t=2.50 s?

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

The intensity of the waves from a point source at a distance d from the source is I . At what distance from the sources is the intensity equal to 2I?

When a certain string is under tension T , the speed of a wave in the string is m What will be the speed of a wave in the string if the tension is increased to 2T without changing the mass or length of the string?

If the angular frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum acceleration of the oscillator change?

A 1.5-kg cart attached to an ideal spring with a force constant (spring constant) of 20 N/m oscillates on a horizontal, frictionless track. At time t = 0.00 s, the cart is released from rest at position x = 10 cm from the equilibrium position. (a) What is the frequency of the oscillations of the cart? (b) Determine the maximum speed of the cart. Where does the maximum speed occur? (c) Find the maximum acceleration of the mass. Where does the maximum acceleration occur? (d) How much total energy does this oscillating system contain? (e) Express the displacement as a function of time using a cosine function.

A 4.0-g string is 0.39 m long and is under tension. The string vibrates at 600 Hz in its third harmonic. What is the tension in this string?

A 25-g string is stretched with a tension of 43 N between two fixed points 12 m apart. What is the frequency of the second harmonic?