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**’.

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**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 ‘ f_{1}’ is
called the ** fundamental frequency**.

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**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__.

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•**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