the speed of a wave in a 4 m rope is 3.2 m/s. what is the frequency of the vibration required to produce a standing wave pattern with
1 antinode?
2 antinodes?
4 antinodes?
please help!!! i don't understand how to do this
To find the frequency of the vibration required to produce a standing wave pattern with a certain number of antinodes, you can use the formula:
f = v / λ,
where:
f is the frequency of the wave,
v is the speed of the wave, and
λ is the wavelength of the wave.
In the case of a standing wave, the wavelength is related to the length of the rope and the number of antinodes. The length of the rope is 4 m.
For a standing wave pattern with "n" antinodes, the wavelength can be calculated using the formula:
λ = 2L / n,
where L is the length of the rope, and n is the number of antinodes.
Let's calculate the frequency for each case:
1. One antinode (n = 1):
λ = 2(4 m) / 1 = 8 m.
f = v / λ = 3.2 m/s / 8 m = 0.4 Hz.
2. Two antinodes (n = 2):
λ = 2(4 m) / 2 = 4 m.
f = v / λ = 3.2 m/s / 4 m = 0.8 Hz.
3. Four antinodes (n = 4):
λ = 2(4 m) / 4 = 2 m.
f = v / λ = 3.2 m/s / 2 m = 1.6 Hz.
So, the frequencies required to produce standing wave patterns with 1 antinode, 2 antinodes, and 4 antinodes are 0.4 Hz, 0.8 Hz, and 1.6 Hz, respectively.