Question

name
calculations using properties of waves
velocity = wavelength x frequency
unit of velocity = m/s
unit of frequency = hertz
unit of wavelength = m
provide the answers to the questions below.

1. if a wave is moving toward shore with a velocity of 10.0 m/s and it has a frequency of 2.5 hertz, what is its wavelength?

answer:

1. if a tuning fork has a frequency of 320 hertz and the wavelength of the sound it produces is 1.5 meters, what is the velocity of the wave.

answer:

1. the speed of light in a vacuum is 3.0 x 10^8 m/s. red light has a wavelength of 7 x 10^{-7}, what is its frequency in a vacuum?

answer: 8.1 x 10^9

1. the frequency of violet light is 7.5 x 10^{14} hertz. what is its wavelength in a vacuum? (note: use the speed of light given in the previous question)

answer:

1. if a jump rope is shaken fast enough to produce a wave with a wavelength of 0.5 m and the crest of the wave passes a specific point 6 times per second, what is the velocity of the wave?

answer:

Explanation:

Step1: Rearrange the formula

Given \(v = \lambda\times f\), we can rearrange it to find \(\lambda=\frac{v}{f}\), \(v=\lambda\times f\) and \(f = \frac{v}{\lambda}\) as needed.

Step2: Solve question 1

For question 1, \(v = 10.0\space m/s\), \(f=2.5\space Hz\). Using \(\lambda=\frac{v}{f}\), we have \(\lambda=\frac{10.0}{2.5}=4\space m\).

Step3: Solve question 2

For question 2, \(\lambda = 1.5\space m\), \(f = 320\space Hz\). Using \(v=\lambda\times f\), we get \(v=1.5\times320 = 480\space m/s\).

Step4: Solve question 3

For question 3, \(v = 3.0\times10^{8}\space m/s\), \(\lambda=7\times 10^{-7}\space m\). Using \(f=\frac{v}{\lambda}\), \(f=\frac{3.0\times 10^{8}}{7\times10^{-7}}\approx4.29\times 10^{14}\space Hz\) (the hand - written answer \(8.1\times10^{9}\) is incorrect).

Step5: Solve question 4

For question 4, \(v = 3.0\times10^{8}\space m/s\), \(f = 7.5\times10^{14}\space Hz\). Using \(\lambda=\frac{v}{f}\), \(\lambda=\frac{3.0\times10^{8}}{7.5\times10^{14}} = 4\times10^{-7}\space m\).

Step6: Solve question 5

For question 5, \(\lambda=0.5\space m\), \(f = 6\space Hz\) (since the crest passes 6 times per second). Using \(v=\lambda\times f\), \(v=0.5\times6=3\space m/s\).

Answer:

1. \(4\space m\)
2. \(480\space m/s\)
3. \(4.29\times 10^{14}\space Hz\)
4. \(4\times 10^{-7}\space m\)
5. \(3\space m/s\)