声速的测量与示波器的使用 理学院

Determining the Velocity of Sound and Using the

Oscilloscope

声速的测量与示波器的使用 理学院

1.Purpose: Understand the relationship between the sound

speed and the air state parameters

Understand the function of the piezoelectricity

transducer. Understand deeply the theory of

standing waves and vibrating interfering

Mastering the using of the oscilloscope.

Mastering a method of measuring sound speed.

声速的测量与示波器的使用 理学院

2.Principle:(1) sound speed in theory is expressed as (1)

In the formula (1), T0=273.15 K ， t is condition temperature, formula (1) can be used to calculate the sound speed in air.

(2) the theory of sound speed measuringBy the relationship between speed v frequency f and wavelength λ: v=fλ (2)so when we measure out f and λ , we can calculate v by formula (2).The instruments are showed in Fig.1.

000 145.3311

T

t

T

tvv

Fig.1 Instruments used to measure λ

声速的测量与示波器的使用 理学院

The transducer S1 is used to emit sound wave . The transducer

S2 is used to receive sound wave. When the standing wave appears,

the sound wave received by S2 is strongest, and the phenomena can

be displaced by the oscilloscope.

A standing wave pattern is an interference phenomenon. It is

formed as the result of the perfectly timed interference of two waves

passing through the same medium. A standing wave pattern is not

actually a wave; rather it is the pattern resulting from the presence of

two waves of the same frequency with different directions of travel

within the same medium.

声速的测量与示波器的使用 理学院

One characteristic of every standing wave pattern is that there are points along the medium which appear to be standing still. These points, sometimes described as points of no displacement, are referred to as nodes. There are other points along the medium which undergo vibrations between a large positive and large negative displacement. These are the points which undergo the maximum displacement during each vibrational cycle of the standing wave. In a sense, these points are the opposite of nodes, and so they are called antinodes. A standing wave pattern always consists of an alternating pattern of nodes and antinodes. The animation shown below depicts a rope vibrating with a standing wave pattern. The nodes and antinodes are labeled on the diagram. When a standing wave pattern is established in a medium, the nodes and the antinodes are always located at the same position along the medium; they are standing still. It is this characteristic which has earned the pattern the name standing wave.

声速的测量与示波器的使用 理学院

The positioning of the nodes and antinodes in a standing wave pattern can be explained by focusing on the interference of the two waves. The nodes are produced at locations where destructive interference occurs. For instance, nodes form at locations where a crest of one wave meets a trough of a second wave; or a half-crest of one wave meets a half-trough of a second wave; or a quarter-crest of one wave meets a quarter-trough of a second wave; etc. Antinodes, on the other hand, are produced at locations where constructive interference occurs. For instance, if a crest of one wave meets a crest of a second wave, a point of large positive displacement results. Similarly, if a trough of one wave meets a trough of a second wave, a point of large negative displacement results.

声速的测量与示波器的使用 理学院

Antinodes are always vibrating back and forth between these

points of large positive and large negative displacement; this is

because during a complete cycle of vibration, a crest will meet a

crest; and then one-half cycle later, a trough will meet a trough.

Because antinodes are vibrating back and forth between a

large positive and large negative displacement, a diagram of a

standing wave is sometimes depicted by drawing the shape of

the medium at an instant in time and at an instant one-half

vibrational cycle later. This is done in the diagram below.

声速的测量与示波器的使用 理学院

Nodes and antinodes should not be confused with crests and troughs. When the motion of a traveling wave is discussed, it is customary to refer to a point of large maximum displacement as a crest and a point of large negative displacement as a trough. These represent points of the disturbance which travel from one location to another through the medium.

An anti-node on the other hand is a point on the medium which is staying in the same location. Furthermore, an anti-node vibrates back and forth between a large upward and a large downward displacement. And finally, nodes and antinodes are not actually part of a wave. Recall that a standing wave is not actually a wave but rather a pattern which results from the interference of two or more waves. Since a standing wave is not technically a wave, an anti-node is not technically a point on a wave. The nodes and antinodes are merely unique points on the medium which make up the wave pattern.

The distance between two continuous antinodes or two continuous nodes is λ/2. So we can get by measuring the distance.

声速的测量与示波器的使用 理学院

3.Devices:ZKY-SSA sound speed measuring instrument

声速的测量与示波器的使用 理学院

COS5020B oscilloscope

声速的测量与示波器的使用 理学院

XD-7S signal generator

声速的测量与示波器的使用 理学院

1.frequency ： f= ±0.05 kHz; Δf=0.05 kHz2.wavelength ：

声速的测量与示波器的使用 理学院

110

)(

110

)(2

30,10

21,1

2

110

jiij

n

ii

SxxA

102

102

10 BA

fv

22 )()(

f

fEr

rE vv

vvv

(1)10λ type A error ：

(3)10λ error ：

(4)λ±Δλ=(Sj-i±Δ10λ)/10= ± mm

(2)

(3)

(4)

mm

(2)10λ type B error ： 2i

2i10B 0.028mm

mm

3.calculating sound speed ：

= m/s

%

= m/s

± m/s

(1)

声速的测量与示波器的使用 理学院

000

)5.16(145.3311

TT

tt vv

4.comparing the theory speed and experiment speed ：

(2) = m/s

(3) = %

(1) = m/s

vvv t

%100/ tvvrE