PHYS 260 Chapter Notes - Chapter 15: Standing Wave

78 views1 pages

apricotworm3

17 Oct 2018

School

University of Maryland

Department

Physics

Course

PHYS 260

Professor

Mohapatra

For unlimited access to Textbook Notes, a Class+ subscription is required.

Document Summary

Velocity of a wave on a string is: The average power of a sinusoidal wave is: where f is tension and (cid:2020)is mass per unit length. =(cid:2019) where v is velocity (cid:2019) is wavelength and f is frequency. This equation is true for (cid:1877)(cid:4666)(cid:1876),(cid:1872)(cid:4667)=(cid:1867)(cid:1871)[(cid:4666) (cid:1872)(cid:4667)] (cid:1877)(cid:4666)(cid:1876),(cid:1872)(cid:4667)=(cid:1867)(cid:1871)2[(cid:4666)(cid:3090) (cid:3021)(cid:4667)] (cid:1877)(cid:4666)(cid:1876),(cid:1872)(cid:4667)=(cid:1867)(cid:1871)(cid:4666)(cid:1876) (cid:1872)(cid:4667) In these equation =(cid:2870)(cid:3090) and =2 using the equation of v above and the equation of k we can rewrite as: The equation of a standing wave with a fixed end at x=0 is: The frequency (f) of a wave at harmonic n is : The frequency of a wave fixed at both ends at harmonic n:

Related Questions

A sinusoidal wave is traveling on a string with speed 20. cm/s. Thedisplacement of the particles of thestring at x = 30 cm isfoundto vary with time according to the equation y = (5.0cm)sin[12.0 - (8.0 s^-1)t]. The linear densityofthe string is 8.0 g/cm.

(a) What is the frequency of the wave?
1

s^-1

(b) What is the wavelength of the wave?
2

cm

(c) Give the general equation giving the transverse displacementofthe particles of the string as a function of position andtime.
y(x,t) = ( 3

cm)sin[( 4

cm^-1)x - (5

s^-1)t]

(d) What is the tension in the string?
6

Can you find theangular wave number andangular frequency in the given equation?How are they related to thewavelength and frequency? Can yourelate the angular wave number andangular frequency to the wavespeed? Can you relate wave speed tothe tension and lineardensity?

Read the eBook
- Section 16.6 Wave Speed on a StretchedString

A string of length 2.50 m is fixed at both ends. When the stringvibrates at a frequency of 85.0 Hz, a standing wave with five loopsis formed.
(a.) Sketch the standing wave on the string.
(b.) How far apart are two adjacent nodes?
(c.) Calculate the wavelength of the waves that travel on thestring?
(d.) Calculate the velocity of waves.
(e.) Determine the fundamental frequency of this

1) The equation of a transverse wave on a string is
y = (2.0mm) sin[(20 m-1)x - (600 s^-1)t]

The tension in the string is 15 N. (a) What is the wave speed?(b) Find the linear density of this string in grams per meter.

2) What phase difference between two identical traveling waves,moving in the same direction along a streched string, results inthe vombined wave having an amplitude 1.50 times that of the commonamplitude of the two combining waves? Express your answer in (a)degress, (b) radians, and (c) wavelengths.

3) A rope, under a tension of 200 N and fixed at both ends,oscillates in a second-harmonic standing wave pattern. Thedisplacement of the rope is given by

y= (0.10 m (sin Ï/2) sin 12Ït,

where x=0 at one end of the rope, x is in meters, and t is inseconds. What are (a) the lenght of the rope, (b) the speed of therope, and (c) the mass of the rope ? (d) If the rope oscillates ina third-harmonic standing wave pattern, what will be the period ofoscillation?

PHYS 260 Chapter Notes - Chapter 15: Standing Wave

Document Summary

Get access

Related textbook solutions

Physics: Principles with Applications

Related Documents

PHYS 260 Lecture Notes - Lecture 3: Fraunhofer Diffraction, Optical Instrument, Waveplate

PHYS 260 Lecture Notes - Lecture 2: The Principles Of Quantum Mechanics, Matter Wave, Louis De Broglie

PHYS 260 Lecture Notes - Lecture 3: Spin Magnetic Moment, Azimuthal Quantum Number, Gyromagnetic Ratio

Related Questions