Question: A 2-m string is fixed at one end and is vibrating in its third harmonic with amplitude 3 cm and frequency 100 Hz. (a) Write

A 2-m string is fixed at one end and is vibrating in its third harmonic with amplitude 3 cm and frequency 100 Hz.

(a) Write the wave function for this vibration.

(b) Write an expression for the kinetic energy of a segment of the string of length dx at a point x at some time t. At what time is this kinetic energy maximum? What is the shape of the string at this time?

(c) Find the maximum kinetic energy of the string by integrating your expression for part (b) over the total length of the string.

Step by Step Solution

★★★★★

3.45 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Using 43 m yx t 003 sin 3x4 cos 200tm b dm dx dK 12v y 2 dm dK 126sin 3x4 s... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

10-P-O-S-W (141).docx

120 KBs Word File

Students Have Also Explored These Related Oscillations Mechanical Waves Questions!

A 4-m-long, 160-g rope is fixed at one end and is tied to a light string at the other end. Its tension is 400 N. (a) What are the wavelengths of the fundamental and the next two harmonics? (b) What...

The wave function for a standing wave is given in Equation 18.3 as y = 2A sin kx cos wt. (a) Rewrite this wave function in terms of the wavelength ' and the wave speed v of the wave. (b) Write the...

The wave function for the hydrogen-atom quantum state represented by the dot plot shown in figure, which has n = 2 and ? = m? = 0, is in which a is the Bohr radius and the subscript on ?(r) gives the...

A string 5 m long that is fixed at one end only is vibrating in its fifth harmonic with a frequency of 400 Hz. The maximum displacement of any segment of the string is 3 cm. (a) What is the...

Lab 13: Waves & interference Learning Objectives Differentiate between types of waves. Understand how to mathematically describe traveling waves. Understand how to model the propagation of a pulse on...

Problem 2 A string with both ends held fixed is Vibrating in its third harmonic. The waves have a speed of 192 In / s and a frequency of 240 Hz. The amplitude of the standing wave at an antinode is...

A string with both ends held fixed is vibrating in its third harmonic. The waves have a speed of 192 m/s and a frequency of 240 Hz. The amplitude of the standing wave at an antinode is 0.400 cm. (a)...

1 5 . 6 8 A string with both ends held fixed is vibrating in its third harmonic. The waves have a speed of 1 9 2 m / s and a frequency of 2 4 0 Hz . The amplitude of the standing wave at an antinode...

Echance 7 ans,valeur nominale 1000$ taux de coupon:16% Tre en juin 1982(date achat): 16% taux reinvestissement an 2 et 3:10% taux reinvestissement an 4 et 5: 8% taux reinvestissement an 6: 7% Tre au...

A string 3 . 5 0 m long and fixed at both ends is vibrating in its third harmonic. The maximum displacement of any point on the string is 4 . 0 0 mm . The speed of transverse waves on this string is...

Buyers have higher market power when: A) their switching costs are low B) they are less concentratedC) firms sell a highly differentiated product D) they are not a significant purchaser of the...

The golf professional at a private course claims that members who have taken lessons from him lowered their handicap by more than five strokes. The club manager decides to test the claim by randomly...

What additional information does a goal - based agent use to decide actions compared to a simple reflex agent? Select one: Descriptions of desirable states ( goals ) . A utility function. An internal...

When the 10-lb plunger is released from rest in its vertical guide at = 0, each spring of stiffness k = 20 lb /in. is uncompressed. The links are free to slide through their pivoted collars and...

The system of three particles has the indicated particle masses, velocities, and external forces. Determine r, r, r , T, HO, and H O for this three-dimensional system. 4m 1.5d F 3v d 2d m 2v -y 2m

1. Recreate Table 19.1 for the following currencies: Australian dollar, British pound, Canadian dollar, Chinese yuan, EMU euro, Japanese yen, and Swiss franc. Be sure to show both the direct...

You work at a victim/witness resource center where you assist the victims of crime to handle the emotional and technical ramifications of the crime before they go to court. The husband of a victim, a...

What is meant by the phase-variable form of the state equation?

What would happen to interest rates on municipal securities, given each of the following scenarios? a. The government increases marginal tax rates. b. The tax exemption on municipals is eliminated....

A rocket is accelerating upward at 4.00 m/s2 from the launch pad on the earth. Inside a small 1.50kg ball hangs from the ceiling by a light 1.10-m wire. If the ball is displaced 8.50 from the...

A square object of mass m is constructed of four identical uniform thin sticks, each of length L, attached together. This object is hung on a hook at its upper comer (Fig. 13.37). If it is rotated...

An object with mass 0.200 kg is acted on by an elastic restoring force with force constant 10.0 N/m. (a) Graph elastic potential energy U as a function of displacement x over a range of x from -...

Grenouille Properties. Grenouille Properties (U.S.) expects to receive cash dividends from a French joint venture over the coming three years. The first dividend, to be paid in one year, is expected...

Tax credits A U.S.-based MNC has a foreign subsidiary that earns $258,000 before local taxes, with all the after-tax funds to be available to the parent in the form of dividends. The applicable taxes...

please only answer the blank, not the excel sheet Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85 . He wants a fixed...