Question

the simulation in the video can be found here: https://phet.colorado.edu/en/simulation/wave - on - a - string

1. what happens to the wavelength when the frequency is increased?
2. what happens to the wavelength when the frequency is decreased?
3. are frequency and wavelength proportional or inversely proportional to each other? support your answer using evidence.
4. draw a wave. label the crest, trough, wavelength, and frequency.
5. what are the units for wavelength?
6. what are the units for frequency?
7. calculate the wavelength of yellow light emitted from a sodium lamp if the frequency is 5.10 x 10^14 hz (5.10 x 10^14 s^-1)
8. what is the wavelength of radiation with a frequency of 1.50 x 10^13 s^-1?
9. what frequency is radiation with a wavelength of 5.00 x 10^-6 cm? hint: you need to convert the centimeters to meters

Explanation:

Step1: Recall the wave - speed formula

The wave - speed formula is $v = \lambda f$, where $v$ is the speed of the wave, $\lambda$ is the wavelength, and $f$ is the frequency. For electromagnetic waves in a vacuum, $v = c=3.00\times 10^{8}\ m/s$.

Step2: Solve for wavelength in question 14

Given $f = 5.10\times 10^{14}\ Hz$ and $c = 3.00\times 10^{8}\ m/s$. From $c=\lambda f$, we can solve for $\lambda$: $\lambda=\frac{c}{f}$. Substitute the values: $\lambda=\frac{3.00\times 10^{8}\ m/s}{5.10\times 10^{14}\ s^{- 1}}\approx5.88\times 10^{-7}\ m$.

Step3: Solve for wavelength in question 15

Given $f = 1.50\times 10^{13}\ s^{-1}$ and $c = 3.00\times 10^{8}\ m/s$. Using $\lambda=\frac{c}{f}$, we substitute the values: $\lambda=\frac{3.00\times 10^{8}\ m/s}{1.50\times 10^{13}\ s^{-1}} = 2.00\times 10^{-5}\ m$.

Step4: Solve for frequency in question 16

First, convert the wavelength $\lambda = 5.00\times 10^{-6}\ cm$ to meters. Since $1\ m=100\ cm$, $\lambda = 5.00\times 10^{-8}\ m$. Then, from $c = \lambda f$, we can solve for $f$: $f=\frac{c}{\lambda}$. Substitute $c = 3.00\times 10^{8}\ m/s$ and $\lambda = 5.00\times 10^{-8}\ m$: $f=\frac{3.00\times 10^{8}\ m/s}{5.00\times 10^{-8}\ m}=6.00\times 10^{15}\ Hz$.

Answer:

1. $\lambda\approx5.88\times 10^{-7}\ m$
2. $\lambda = 2.00\times 10^{-5}\ m$
3. $f = 6.00\times 10^{15}\ Hz$