Question

swyk: wave calculations
the speed of sound in air is about 340 m/s. what is the wavelength of sound waves produced by a guitar string vibrating at 490 hz?

Explanation:

Step1: Recall wave speed formula

The formula relating wave speed (\(v\)), frequency (\(f\)), and wavelength (\(\lambda\)) is \(v = f\lambda\). We need to solve for \(\lambda\), so we rearrange the formula to \(\lambda=\frac{v}{f}\).

Step2: Substitute given values

We know that \(v = 340\space m/s\) and \(f = 490\space Hz\). Substituting these values into the formula, we get \(\lambda=\frac{340}{490}\).

Step3: Calculate the wavelength

Performing the division, \(\lambda\approx0.694\space m\) (rounded to three decimal places).

Answer:

The wavelength of the sound waves is approximately \(0.69\space m\) (or more precisely \(\frac{340}{490}\approx0.694\space m\)).