A transverse wave is observed to be moving along a lengthy rope. Adjacent crests are positioned 2.4m apart. Exactly six crests are observed to move past a given point along the medium in 9.1 seconds. Determine the wavelength, frequency and speed of these waves.
tHank you :)
wavelength: 2.4m
frequency: 6/9.1s
speed: 2.4 m * 6/9.1s = ? m/s
Well, isn't that a knotty question! Let's unravel it together, shall we?
Given that adjacent crests are 2.4m apart, we can infer that this distance represents one full wavelength (λ) of our transverse wave.
Now, we are told that exactly six crests pass a specific point in 9.1 seconds. Since the number of crests passing is directly related to the frequency (f) of the wave, we can conclude that the frequency is 6/9.1 Hz (crests/seconds).
To determine the speed (v) of the wave, we can use the equation v = λ * f. Substituting the values we have, v = 2.4m * (6/9.1) Hz.
If you crunch the numbers, you'll find that the wavelength (λ) is 2.4m, the frequency (f) is approximately 0.659 Hz, and the speed (v) is approximately 1.574 m/s. Voila!
Keep those waves rollin'!
To solve this problem, we can use the formulas:
Speed (v) = Wavelength (λ) * Frequency (f)
Wavelength (λ) = Distance between crests
Frequency (f) = Number of crests passed / Time taken
Given:
Distance between adjacent crests (λ) = 2.4 m
Number of crests passed in a given time (N) = 6
Time taken (t) = 9.1 s
1. Determine the wavelength (λ):
The distance between adjacent crests is the wavelength.
λ = 2.4 m
2. Determine the frequency (f):
We can calculate the frequency by dividing the number of crests by the time taken.
f = N / t
= 6 / 9.1
≈ 0.659 Hz (rounded to three decimal places)
3. Determine the speed (v):
The speed of the waves can be calculated by multiplying the wavelength by the frequency.
v = λ * f
= 2.4 * 0.659
≈ 1.577 m/s (rounded to three decimal places)
Therefore, the wavelength is 2.4 m, the frequency is approximately 0.659 Hz, and the speed is approximately 1.577 m/s.
To determine the wavelength, frequency, and speed of the transverse wave on the rope, we can use the following formulas:
1. Wavelength (λ) = Distance between adjacent crests
2. Frequency (f) = Number of crests passing a point per unit time
3. Speed (v) = Wavelength × Frequency
Given information:
- Distance between adjacent crests (wavelength) = 2.4 m
- Number of crests passing a point = 6
- Time taken for the crests to pass a point = 9.1 seconds
To find the wavelength:
The distance between adjacent crests is given as 2.4 m. Therefore, the wavelength (λ) is 2.4 m.
To find the frequency:
The number of crests passing a point in 9.1 seconds is given as 6. To find the frequency, we divide the number of crests by the time:
Frequency (f) = Number of crests / Time = 6 / 9.1 seconds = 0.659 Hz (approximately)
To find the speed:
The speed (v) of a wave is given by the equation:
Speed (v) = Wavelength (λ) × Frequency (f)
Substituting the known values:
Speed (v) = 2.4 m × 0.659 Hz = 1.57 m/s (approximately)
Therefore, the wavelength of the waves on the rope is 2.4 meters, the frequency is 0.659 Hz, and the speed is 1.57 m/s.