The distance between the second and sixth crests in a wave is 75cm and one crest travels a distance of 25 cm in 3.0s . Find the frequency of the wave
The distance across four waves is 75 cm, therefore,
λ = 18.75 cm
Δd = 25 cm
Δt = 3.0 s
f =?
v = Δd
Δt
= 25 cm
3.0 s
= 8.333 cm/s
v = fλ
f = v
λ
= 8.333 cm/s
18.75 cm
= 0.4444 s−1
= 0.4444 Hz
To find the frequency of the wave, we can use the formula:
Frequency = Speed / Wavelength
First, let's find the wavelength of the wave.
Given: The distance between the second and sixth crests is 75 cm.
The distance between two consecutive crests is half of the wavelength, so we can calculate the wavelength:
Wavelength = (Distance between second and sixth crests) / (Number of crests - 1)
= 75 cm / (6 - 2)
= 75 cm / 4
= 18.75 cm
Next, let's find the speed of the wave.
Given: One crest travels a distance of 25 cm in 3.0 seconds.
Speed = Distance / Time
= 25 cm / 3.0 s
= 8.33 cm/s
Now that we have both the speed and wavelength, we can calculate the frequency using the formula:
Frequency = Speed / Wavelength
= 8.33 cm/s / 18.75 cm
= 0.444 Hz
Therefore, the frequency of the wave is approximately 0.444 Hz.
Well, the distance between the second and sixth crests is 75 cm, right? And if we know that one crest travels a distance of 25 cm in 3.0 seconds, we can use this information to find the frequency of the wave.
To find the frequency, we need to know how many crests pass a given point in a certain amount of time. In this case, we are given the distance between the second and sixth crests, which is 75 cm. So, the total distance traveled by the wave is 75 cm.
Now, let's think about the distance traveled by one crest in 3.0 seconds. We know that one crest travels a distance of 25 cm in this time. So, the time it takes for the wave to travel a distance of 75 cm is 3.0 seconds * 3 crests = 9.0 seconds.
Now we can find the frequency using the formula: frequency = 1/time. Plugging in the values, we get: frequency = 1/9.0 s = 0.111 Hz.
So, the frequency of the wave is approximately 0.111 Hz. But hey, don't worry, it won't try to serenade you with a low-pitched wave song!
drdhd
λ=0.3 m.
v=s/t =0.25/3 m/s.
λ =v/f,
f=v/λ =0.25/3•0.3 =0.28 Hz