Standing Waves

Lecture 2

Standing Waves

If waves are confined in space, reflections at both ends cause the waves to travel in both directions, and they superimpose. This result in a stationary vibration pattern called Standing Waves.

 

Example:

Electron standing waves patterns inside the letter O and U. This OU atomic logo is written by individual silver atoms on a silver surface at pressure = 10-11 Torr, and temperature of 4.2 K. Actual image size: ~40 nm x 24 nm.

(Courtesy of Dr. S.-W. Hla, Ohio University).

 

Standing Waves on a String.

 

,

,

 

l = wave length,

w = angular frequency,

L = the length of string,

f = frequency,

v = velocity.

 

The frequency associated with n=1 or f1 is called the fundamental frequency.

 

Example Problems

Example 16-3

Two sources oscillate in phase. At a point 5 m from one source and 5.17 m from the other, the amplitude of sound source separately is A. Find the amplitude of the resultant wave if the frequency of the sound wave is

a). 1000 Hz.

b). 2000 Hz.

 

 

Two Loud Speakers

Two loud speakers are separated by a distance of 6.5 m. A listener sits directly in front of one speaker at a distance of 8.7 m so that the two speakers and the listener form a right triangle. Find the lowest frequency for which the path difference from the speakers to the listener is an odd number of half-wavelength.

 

 

59/528

A violin string of length 40 cm and mass 1.2 g has a frequency of 500 Hz when it is vibrating in its fundamental mode.

a). What is the wavelength of the standing wave on the string?

b). What is the tension in the string?

c). Where should you place your finger to increase the frequency to 650 Hz?

 

 

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Dr. S.-W. Hla