PhysicsNTHUMFTai-戴明鳳

Lab. 8A - String Vibration ( 弦振盪 )

Standing wave in stationary medium. The red dots represent the wave nodes.

http://en.wikipedia.org/wiki/Standing_wave

I. Object ( 目的 )

To obersve that a vibration in a string is a wave. Usually a vibrating string produces a sound whose frequency in most cases is constant. Therefore, since frequency characterizes the pitch, the sound produced is a constant note. Vibrating strings are the basis of any string instrument like guitar, cello, or piano.

Vibration and standing waves in a string, The fundamental and the first 6 overtones.http://en.wikipedia.org/wiki/Standing_wave

PhysicsNTHUMFTai-戴明鳳

Vibrating String The fundamental vibrational mode of a stretched string is such t

hat the wavelength is twice the length of the string. The basic wave relationship and wave velocity are given

The string will also vibrate at all harmonics of the fundamental. Each of these harmonics will form a standing wave on the string.

PhysicsNTHUMFTai-戴明鳳

An ideal vibrating string Will vibrate with its fundamental frequency and all har

monics of that frequency. The position of nodes and antinodes is just the opposit

e of those for an open air column. The fundamental frequency

The harmonics are integer multiples.

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A resonant standing wave on a soft string.

It is driven by a vibrator at 120 Hz.

For strings of finite stiffness, the harmonic frequencies will depart progressively from the mathematical harmonics.

To get the necessary mass for the strings of an electric bass, wire is wound around a solid core wire.

This allows the addition of mass without producing excessive stiffness.

PhysicsNTHUMFTai-戴明鳳

Rotating saturn hexagon The hexagonal cloud feature at the north pole of

Saturn is thought by most astronomers to be some sort of standing wave pattern.

Rotatingsaturnhexagon.gif from http://en.wikipedia.org/wiki/Standing_wave

PhysicsNTHUMFTai-戴明鳳

原理 :

設一根均勻弦線，長 L, 質量 M,

單位長度質量密度 = M/L = m/l

兩端固定繃緊 , 張力 T

則弦振動時通過弦波 ( 橫波 )

之波速 ( 以脈波為例 ) vT

Fnet = 2·F sin ~ 2F (for small angle )

= 2F [(l/2)/R]

= v2/R

= ( l)v2/R

T F = v2

目的 : 求弦振動 (string vibration)時

之波速、波長及頻率

PhysicsNTHUMFTai-戴明鳳

梅爾德裝置 (Melde Device)

(1) 滑輪(2) 砝碼 m(3) 弦線：一端固定於 (7) 直

立或橫擺音叉上(4) 電磁鐵(5) 白金接點(6) 可變直流電源(7) 直立或橫擺音叉：經可變

直流電源 (6) 及電磁鐵 (4) ，可使白金接點 (5) 振動產生特定頻率 f

令一端經滑輪 (1) 用砝碼 m(2)使絃線固定繃緊 , 張力 T = mg則弦振動時之波速 vmg f 波波

測量波長 進行波 ( 以正弦波為例 , 波方向 x 軸 , 弦位移 y 軸 / 橫波 ) y(x,t) = ymsin[2(x/ – ft)] = ymsin(kx – t)波向量 (wave vector): k = 2角頻率 : = 2f

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調整弦長 L 及張力 T (= mg), 使音叉端之入射波與反射端之反射波重疊成駐波 (standing wave)

1.結點 (node) ：位移 y = 0 點，音叉端及反射端固定 , 位移亦為零

2.反結點 (antinode) ：位移最大 y = ym 點

3.波長 : = 2L/n (n: 反結點數 )

4.音叉頻率 : f = v/= (n/2L)(mg/)1/2

f

L

m