Question

1. A continuous wave with a wavelength of 43 m is traveling through air at 329 m/s. If another wave, with twice the frequency of the first, is traveling through the same medium what is the wavelength of the second wave?

2. Two waves are traveling through the air simultaneously. Wave 1 has a frequency of 541 Hz and a wavelength of 9.81 m. Wave 2 has a wavelength of 9.34 m. What is the frequency of wave 2?

Answer 1

1. The speed of the wave is equal to the wavelength times the frequency. For the first wave, we have:

v = λf

where v is the speed of the wave, λ is the wavelength, and f is the frequency. Solving for the frequency, we get:

f = v/λ = 329 m/s / 43 m = 7.65 Hz

The frequency of the second wave is twice that of the first wave, so its frequency is:

f' = 2f = 2(7.65 Hz) = 15.3 Hz

To find the wavelength of the second wave, we use the same formula:

v = λ'f'

where λ' is the wavelength of the second wave. Solving for λ', we get:

λ' = v/f' = 329 m/s / 15.3 Hz = 21.5 m

Therefore, the wavelength of the second wave is 21.5 m.

2. The speed of the wave is equal to the wavelength times the frequency. For wave 1, we have:

v = λf = 541 Hz * 9.81 m = 5310.21 m/s

For wave 2, we know the wavelength, but not the frequency. We can rearrange the formula to solve for the frequency:

f = v/λ = 5310.21 m/s / 9.34 m = 568.8 Hz

Therefore, the frequency of wave 2 is 568.8 Hz.