Question

A drummer plays a note with a frequency of 85 Hz. What is the wavelength of this sound wave in air? (Speed of sound in air = 340 m s-1)​

Answer 1

`4.0\; {\rm m}`.

Step-by-step explanation:

The speed
`v` of a wave is the distance the wave travels in unit time.

The frequency
`f` of a wave is the number of cycles completed in unit time. Note that
`1\; {\rm Hz} = 1\; {\rm s^(-1)}`. Thus, for the wave in this question, frequency would be
`f = 85\; {\rm Hz} = 85\; {\rm s^(-1)}`.

The wavelength
`\lambda` of the wave is the distance travelled in each cycle of the wave. To find wavelength, divide the speed of the wave (distance travelled in unit time) by the frequency of the wave (number of cycles included in that much distance.)

`\begin{aligned}\lambda &= (v)/(f) \\ &= \frac{340\; {\rm m\cdot s^(-1)}}{85\; {\rm s^(-1)}} \\ &\approx 4.0\; {\rm m}\end{aligned}`.