Hold the tuning fork very close to the microphone, almost touching it. One of the best things to do to improve the signal from a tuning fork is to hold it so that the outside of the tuning fork is parallel to the face of the microphone. Many times people try pointing the tuning fork at the microphone, but the side of the microphone will actually produce a cleaner signal.
Another common problem is the timing of the experiment. When sampling at a high frequency, you are usually only collecting data for a very short amount of time. Be sure to strike the tuning fork first, get it in position, THEN quickly start your data run. This way, you know that the sound signal will already be reaching the microphone when your data run starts.
Keep in mind the relationship between the sampling frequency and the signal. You need to be sampling at about 5 times the rate of the highest frequency signal you want to detect. So, if you are using a 400 Hz tuning fork, you need to be collecting data at at least 2000 samples/second in order to get enough of the sine wave to see it clearly on the screen.
The method used to strike the tuning fork will directly affect how clean your waveform is. We suggest striking the fork about 2/3 of the way down the side towards the base. Strike it against an object that is not real hard. Many people use something made of rubber, such as a shoe sole or rubber mallet. Other people prefer to strike the tuning fork on an object like their kneecap.
Because the waveform will be a function of how the fork is struck, there is an element of experimental skill involved in getting a clean waveform. If the sound is bright to the ear, the strike was almost certainly a poor one that will give a waveform rich in undesired harmonics.
An excellent alternative to using a tuning fork is to use an inexpensive electronic keyboard set to the flute sound. This sidesteps the problem of bad tuning fork strikes. We prefer a keyboard for demonstrations over tuning forks.
The microphone is fairly sensitive. If you can do anything to reduce ambient noise, you will almost always get cleaner data.