Calculating Sound Waves in Mayonnaise
Aug 20, 2021

Universal Wave Equation Example

According to r/EngineeringStudents, the speed of sound in mayonnaise is 2613 $$\textrm{ms}^{-1}$$. According to Scientific American, a soprano's frequency range could be between 250 and 1500 Hz, so let's see what the wavelength of a 1200 Hz soprano tone would be as it passes through mayonnaise. For simplicity, we'll use the scalar wave speed instead of vector velocity.

$v = \lambda f$

Insert values.

$2613 \textrm{ ms}^{-1} = \lambda (1200 \textrm{ Hz}).$

Divide both sides by 1200 to solve for $$\lambda$$.

$\therefore \lambda = \frac{2613\textrm{ ms}^{-1}}{1200\textrm{ Hz}} \approx 2.18 \frac{\textrm{m}}{\textrm{s Hz}}.$

Since Hz $$= \frac{1}{\textrm{s}}$$, the units cancel and our answer is 2.18 m.

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