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Waves
 
Aim: to measure the Wavelength and Velocity of Propagation of Ultra-Sound Waves
See Longitudinal Wave, Relation between Wavelength, Frequency and Velocity
 
The term ultra-sound refers to longitudinal waves (usually in air) which have a frequency which is too high for them to be detected by the human ear.
The u.s. transmitters used in these experiments have a frequency of 40kHz (the highest frequency you can hear is certainly less than 20kHz).
Ultra-sound transmitters and receivers are readily and cheaply available and have the advantage that they allow you to perform experiments on sound... without annoying your neighbours!
 
Too experiments are suggested here:
- find the wavelength of the u.s. by a method involving interference
- a direct method of measuring the velocity of propagation (using velocity = distance/time)
 
For the first experiment the receiver can be connected to either an amplifier and a.c. voltmeter or an oscilloscope.
For the second experiment, a dual beam oscilloscope is helpful.
 
Method
The first experiment is analogous to Young's experiment with light.
Use two transmitters, connected to the same generator, to produce an interference pattern which can be observed using the single, movable receiver.
By moving the receiver along the direction indicated by the arrows, find the distance between adjacent maxima of the interference pattern (this is equivalent to the fringe spacing in Young's experiment)
Once this distance is known we can find the wavelength (see here if necessary).
NB if you restrict measurements to near the central maximum (and the distance between transmitters and receiver is relatively large), then you should be justified in using the approximation that sinθ=θ for small angles.
In the second experiment (to measure the velocity of propagation of the waves), we use two receivers and one transmitter, as shown in the next diagram. 
Notice that we now set the signal generator to "square wave" output (at a frequency of about 300Hz).
 
The sharp pulses emitted by the transmitter set the receivers oscillating at their resonant frequency (usually 40kHz but check manufacturer's information).
Therefore you should see two damped oscillations on the oscilloscope screen.
Point A is connected to one input of the oscilloscope, point B to the other input and G to oscilloscope ground.
 
Use the oscilloscope to find the difference between the times of arrival of the transmitted pulses at the two receivers, for a range of distances, s.
 
Having measured the wavelength in experiment 1 and the velocity in experiment 2, you can now see if your measurements agree with the equation relating frequency, velocity and wavelength.
 
Alternative Method for Measuring the Wavelength
This method is based on observing Lissajous figures on the oscilloscope screen produced by using one receiver to produce horizontal deflections of the electron beam and the other to produce vertical deflections.
 
Before starting, put the oscilloscope in X-Y mode and signal generator back to "sine wave" output.
With the two receivers close together and equidistant from the transmitter, you should be able to obtain a straight line at (about) 45 on the oscilloscope screen.
Move either of the receivers slowly nearer to or further away from the transmitter (along the direction shown in the diagram).
Stop when you have a straight line at 90 to the previous line.
Congratulations, you have now moved that receiver through a distance equal to half a wavelength.
 
I assume you now see how to measure the wavelength by this method!
 
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