Question

swyk: wave calculations
the note a above middle c on a piano emits a sound wave with a wavelength of 0.77 meters. what is the frequency of the wave? use 340 m/s as the speed of the sound wave.

0 / 10000 word limit

Explanation:

Step1: Recall the wave speed formula

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

Step2: Substitute the given values

We know that the speed of the sound wave \(v = 340\space m/s\) and the wavelength \(\lambda= 0.77\space meters\). Substituting these values into the formula for frequency, we get \(f=\frac{340}{0.77}\).

Step3: Calculate the frequency

Performing the division \(\frac{340}{0.77}\approx441.56\space Hz\) (rounded to two decimal places).

Answer:

The frequency of the wave is approximately \(441.56\space Hz\) (or more precisely, \(\frac{340}{0.77}\approx441.56\space Hz\)).