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STANDING WAVES Phys 101 LO6 / March 8, 2015 By Shushan Deng

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STANDING WAVESPhys 101 LO6 / March 8, 2015 By Shushan Deng

WHAT IS A STANDING WAVE?

A standing wave is a vibration in which certain points of the wave remain fixed, while other points oscillate to maximum amplitude.

The nodes of a standing wave remain at amplitude=0, while the points between the nodes (the anti-nodes) move with maximum amplitude

WHAT CAN CAUSE A STANDING WAVE PATTERN?

Standing wave patterns can occur when vibrations move along a taut string.

Waves are reflected back and forth between the fixed ends of the string, when the string is plucked or disturbed

An example of this can be found in plucking guitar strings

STANDING WAVES ON STRINGS

Harmonics refer to the associated patterns and frequencies of the standing waves

The fundamental frequency, also known as first harmonic, is the lowest frequency of the standing wave pattern

The equation for frequency, f, can be given as such: f = √(T/µ) where T=Tension and µ=linear mass density

Fundamental, first harmonic

Second harmonic

n=1

n=2

QUESTION 1

The answer is c) 450 Hz.

This is because the frequency of a harmonic is “n” times the frequency of the fundamental, where “n” is an integer. A frequency of the third harmonic would be 3 times the value of the fundamental.

f3 = 3*f1 = 3*150 Hz = 450 Hz.

The fundamental frequency of a stretched string is 150 Hz. The frequency of the third harmonic is ________.

a) 250 Hz

b) 350 Hz

c) 450 Hz

d) 550 Hz

QUESTION 2

The answer is b) Destructive interference

Since nodes always remain at amplitude=0, their displacement also remains at zero. This zero displacement is possible because of destructive interference.

A node is a point along the wave in which there is ________.

a) Maximum amplitude

b) Destructive interference

c) Constructive interference

QUESTION 3

We know that the distance between consecutive nodes is half a wavelength. From the first and fourth nodes, the distance is one and a half (1.5) wavelengths.

(40.0 cm / 1.5 ) = 26.7 cm

The wavelength of the original wave is 26.7 cm.

A person playing guitar creates a standing wave by plucking a string. If the distance between the first and fourth nodes is 40.0 cm, then what is the wavelength of the original wave?

Thank you!