A long rope is fixed at one end and the free end is made to oscillate in one plane at right angles to the rope with a frequency of 4hertz. The successive crest at 0.6meter apart
calculate the speed of the waves. For what frequency would the wavelength be 30cm?
1. To calculate the speed of the waves, we can use the wave equation: v = f * λ
where v is the speed of the waves, f is the frequency, and λ is the wavelength.
We are given the frequency (f = 4 Hz) and the distance between successive crests (λ = 0.6 m).
Using the wave equation:
v = 4 Hz * 0.6 m
v = 2.4 m/s
The speed of the waves is 2.4 m/s.
2. To find the frequency for a wavelength of 30 cm (0.3 m), we can rearrange the wave equation to solve for f:
f = v / λ
We are given the speed of the waves (v = 2.4 m/s) and the wavelength (λ = 0.3 m).
Using the wave equation:
f = 2.4 m/s / 0.3 m
f = 8 Hz
The frequency for a wavelength of 30 cm is 8 Hz.
Why did the rope become a comedian? Because it wanted to tie everyone up in knots with its oscillating humor!
But don't worry, I'm here to help untangle the problem. Let's do some calculations!
To calculate the speed of the waves, we can use the formula:
Speed = Frequency × Wavelength
First, let's find the wavelength. The problem states that the successive crest (wave peak) is 0.6 meters apart. This means the distance between consecutive crests is the wavelength. Therefore, the wavelength is 0.6 meters.
Now let's plug in the values:
Speed = 4 Hz × 0.6 m
Speed = 2.4 m/s
So, the speed of the waves is 2.4 meters per second.
Now, let's move on to the second part of the question. We need to find the frequency when the wavelength is 30 cm (which is equal to 0.3 meters).
Rearranging the formula, we have:
Frequency = Speed / Wavelength
Plugging in the values:
Frequency = 2.4 m/s / 0.3 m
Frequency = 8 Hz
So, when the wavelength is 30 cm, the frequency of the waves would be 8 Hz.
I hope these answers didn't "knot" your brain too much!
To calculate the speed of the waves, we can use the formula:
speed (v) = frequency (f) × wavelength (λ)
Given:
Frequency (f) = 4 Hz
Wavelength (λ) = 0.6 meters
Substituting the values into the formula, we have:
v = f × λ
v = 4 Hz × 0.6 meters
v = 2.4 meters per second
So, the speed of the waves is 2.4 meters per second.
Now, let's calculate the frequency for a wavelength of 30 cm.
Wavelength (λ) = 30 cm = 0.3 meters
Using the same formula as before:
v = f × λ
2.4 meters per second = f × 0.3 meters
Rearranging the formula to solve for frequency (f):
f = v / λ
f = 2.4 meters per second / 0.3 meters
f = 8 Hz
Therefore, the frequency required for a wavelength of 30 cm is 8 Hz.
To calculate the speed of the waves, we can use the formula:
Speed = Frequency x Wavelength
First, let's find the wavelength for the given situation:
Since the oscillations of the rope are in one plane at right angles to the rope, we can consider the distance between two consecutive crests as one wavelength.
Given that the successive crests are 0.6 meters apart, the wavelength will also be 0.6 meters.
Now, let's calculate the speed of the waves:
Speed = Frequency x Wavelength
= 4 Hz x 0.6 m
= 2.4 m/s
Therefore, the speed of the waves is 2.4 meters per second.
Next, let's calculate the frequency when the wavelength is 30 cm:
We know that the speed of the waves remains constant. So, we can rearrange the formula for speed:
Frequency = Speed / Wavelength
Given that the wavelength is 30 cm, we need to convert it to meters:
Wavelength = 30 cm = 30/100 m = 0.3 m
Now, let's calculate the frequency:
Frequency = Speed / Wavelength
= 2.4 m/s / 0.3 m
= 8 Hz
Therefore, when the wavelength is 30 cm, the frequency of the wave will be 8 Hz.