Hot chocolate effect . Tap a metal spoon inside a mug of water and note the freq

Question

Hot chocolate effect. Tap a metal spoon inside a mug of water and note the frequency fi you hear. Then add a spoonful of powder (say, chocolate mix or instant coffee) and tap again as you stir the powder. The frequency you hear has a lower value fs because the tiny air bubbles released by the powder change the water's bulk modulus. As the bubbles reach the water surface and disappear, the frequency gradually shifts back to its initial value. During the effect, the bubbles don't appreciably change the water's density or volume or the sound's wavelength. Rather, they change the value of dV/dp

Explanation / Answer

frequency is directly proportional to sqrt of bulk modulus

so ratio of bulk modulus = (dV/dp)s/(dV/dp)i = sqrt(0.539) = 0.734

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