Question

Two waves travel in the same medium at the same speed. one has wavelength 0.0382 m and frequency 9.67×10^6 hz. the other has wavelength 0.04460000398122414 m. what is the period of the second wave?

Answer 1

The relationship between wavelength, frequency and speed of a wave is

`v=\lambda f` (1)
where v is the speed,
`\lambda` is the wavelength and f the frequency.

By plugging the data of the first wave into the equation, we find the speed of the first wave

`v=(0.0382 m)(9.67 \cdot 10^6 Hz)=3.69 \cdot 10^5 m/s`

The problem says the two waves have same speed, so this is also the wave of the second speed.
By using again eq.(1), we can find the frequency of the second wave: (I take only the first digits for the wavelength)

`f= (v)/(\lambda)= (3.69 \cdot 10^5 m/s)/(0.0446 m) = 8.28 \cdot 10^6 Hz`

And its period is the reciprocal of its frequency:

`T= (1)/(f)= (1)/(8.28 \cdot 10^6 Hz)=1.21 \cdot 10^(-7) s`