A sound wave is a longitudinal mechanical wave that follows the wave equation. Use the wave equation to solve these problems on your own. Come back here to check your work.
The Wave Equation
\(\large\mathsf{ v = \lambda f = \frac{\lambda}{T}}\)
| Problem | Picture | Given/Find | Equation | Solution |
|---|---|---|---|---|
| You blow across a soda bottle and the sound emitted has a frequency of 255 Hz. If the sound is moving through air at room temperature, what is the wavelength of that sound wave? |
|
\(\mathsf{ v = 343 \text{ m/s}}\) \(\mathsf{ f = 255 \text{ Hz} }\) \(\mathsf{ \lambda = ? \text{ m} }\) |
\(\mathsf{ v = \lambda f }\) | \(\mathsf{ 343 \text{ m/s} = \lambda (255 \text{ Hz}) }\) \(\mathsf{ \lambda = \frac{343 \text{ m/s}}{255 \text{ Hz}} }\) \(\mathsf{ \lambda = 1.34 \text{ m} }\) |
| A violin plays a note with a frequency of 415.3 Hz with a wavelength of 0.831 m. What is the speed of that sound wave? |
|
\(\mathsf{ v = ? \text{ m/s}}\) \(\mathsf{ f = 415.3 \text{ Hz} }\) \(\mathsf{ \lambda = 0.831 \text{ m} }\) |
\(\mathsf{ v = \lambda f }\) | \(\mathsf{ v = (0.831 \text{ m})(415.3 \text{ Hz}) }\) \(\mathsf{ v = 345 \text{ m/s} }\) |
| A sound wave passing through wood (speed of sound in wood is 3960 m/s) moves with a wavelength of 9.00 m. What is the frequency of the sound created? |
|
\(\mathsf{ v = 3960 \text{ m/s}}\) \(\mathsf{ f = ? \text{ Hz} }\) \(\mathsf{ \lambda = 9.00 \text{ m} }\) |
\(\mathsf{ v = \lambda f }\) | \(\mathsf{ 3960 \text{ m/s} = 1.74 \times 10^6 \text{ m} (f) }\) \(\mathsf{ f = \frac{3960 \text{ m/s}}{9.00 \text{ m}} }\) \(\mathsf{ f = 440. \text{ Hz} }\) |
| The highest note on a piano has a frequency of 4186 Hz. What is the wavelength of that note (assume in room temperature air)? |
|
\(\mathsf{ v = 343 \text{ m/s}}\) \(\mathsf{ f = 4186 \text{ Hz} }\) \(\mathsf{ \lambda = ? \text{ m} }\) |
\(\mathsf{ v = \lambda f}\) | \(\mathsf{ 343 \text{ m/s} = \lambda (4186 \text{ Hz}) }\) \(\mathsf{ \lambda = \frac{343 \text{ m/s}}{4186 \text{ Hz}} }\) \(\mathsf{ \lambda = 0.08194 \text{ m} }\) |
