Question

the average wavelength in a series of ocean waves is 15.0 m. a wave crest arrives at the shore on average every 10.0 s, so the frequency is 0.100 hz. what is the average speed of the waves?
green light has a wavelength of 5.20 × 10⁻⁷ m. the speed of light is 3.00 × 10⁸ m/s. calculate the frequency of green light waves with this wavelength.
the speed of sound in air is about 340 m/s. what is the wavelength of a sound wave with a frequency of 220 hz (on a piano, the a below middle c)?

Explanation:

Step1: Recall the wave speed formula

The formula for the speed of a wave is \(v = f\lambda\), where \(v\) is the speed, \(f\) is the frequency, and \(\lambda\) is the wavelength.

Step2: Substitute the given values for the first problem

Given \(\lambda = 15.0\space m\) and \(f=0.100\space Hz\). Substitute into \(v = f\lambda\): \(v=(0.100\space Hz)\times(15.0\space m)\)

Step3: Calculate the value for the first problem

\(v = 1.50\space m/s\)

Step4: Rearrange the formula for the second problem

From \(v = f\lambda\), we can solve for \(f\) as \(f=\frac{v}{\lambda}\). Given \(v = 3.00\times10^{8}\space m/s\) and \(\lambda=5.20\times 10^{-7}\space m\)

Step5: Substitute and calculate for the second problem

\(f=\frac{3.00\times 10^{8}\space m/s}{5.20\times 10^{-7}\space m}\approx5.77\times 10^{14}\space Hz\)

Step6: Rearrange the formula for the third problem

From \(v = f\lambda\), solve for \(\lambda\) as \(\lambda=\frac{v}{f}\). Given \(v = 340\space m/s\) and \(f = 220\space Hz\)

Step7: Substitute and calculate for the third problem

\(\lambda=\frac{340\space m/s}{220\space Hz}\approx1.55\space m\)

Answer:

1. \(1.50\space m/s\)
2. \(5.77\times 10^{14}\space Hz\)
3. \(1.55\space m\)