Hot Chocolate Experiment: Conclusions Have you ever stirred your hot chocolate and noticed that the pitch increases as you continue to tap?  Here are recordings of the tapping sound under different conditions. Null Hypothesis #1:  There is no substantial difference in the tapping pitch characteristics among different kinds of mugs. In my opinion, this null hypothesis is true.  In general, the pitch increases as you tap the cup.  Admittedly, the shape of the cup does seem to impact the starting pitch.  (The wider mug starts at a lower pitch than the narrower mug.)  Additionally, a separate experiment may be warranted to study the rate of change in pitch.  But for the qualitative purposes here, it seems that the null hypothesis is true.  The shape of the mug is not a factor. Null Hypothesis #2:  There is no difference in the tapping pitch characteristics among different kinds of liquids. This null hypothesis is not true.  Therefore the liquid does make a difference.  The hot water has a high pitch and stays at a high pitch.  The fresh cocoa has a large change in pitch.  The cocoa no longer has a pitch change after it has sat for a while (homogenized).  Question: Why do you think that the fresh cocoa's pitch changes as the spoon taps the mug? Null Hypothesis #3:  There is no substantial difference between cups with or without marshmallows. This null hypothesis is true.  There does not seem to be a great difference between fresh cocoa with marshmallows and without.  But maybe this experiment should be repeated with homogenized cocoa?  If the tapping's pitch is constant with homogenized cocoa, but starts changing after fresh marshmallows are added, then perhaps the marshamallows create the kind of heterogeneity in the mixture that results in a changing pitch?   Back to the main page.