the distance between two successive crests in waves is 1.50m, and the source generates 25 crests and 25 troughs in 5.00sec. what is the speed of the waves?
To find the speed of the waves, we need to determine the wavelength and the time it takes for one complete wave cycle.
1. Calculate the wavelength:
The distance between two successive crests (or troughs) is the wavelength (λ) of the wave. In this case, the distance is given as 1.50 meters.
So, the wavelength (λ) = 1.50 m.
2. Calculate the time for one complete wave cycle:
To calculate the time for one complete wave cycle, we need to find the time it takes for one crest (or trough) to occur.
In this case, we know that in 5.00 seconds, there are 25 crests and 25 troughs. So, the number of wave cycles is 25.
Time for one complete wave cycle (T) = Total time / Number of wave cycles
T = 5.00 s / 25
T = 0.20 s
3. Calculate the speed of the waves:
The speed of a wave is given by the formula: speed (v) = wavelength (λ) / time (T).
v = λ / T
v = 1.50 m / 0.20 s
Now let's calculate the speed:
v = 7.5 m/s
Therefore, the speed of the waves is 7.5 m/s.
To determine the speed of the waves, we need to find the wavelength (distance between two successive crests) and the time it takes for those crests to occur.
Step 1: Find the wavelength (λ)
Given that the distance between two successive crests is 1.50m, we can use this value as the wavelength (λ) of the wave.
Wavelength (λ) = 1.50m
Step 2: Find the time taken for 25 crests and troughs (T)
We are given that the source generates 25 crests and 25 troughs in 5.00 seconds. Since each crest and trough pair is one complete wave, the time taken for 25 crests and troughs is also the time taken for 25 waves.
Time (T) = 5.00s
Step 3: Calculate the speed of the waves (v)
The formula for calculating the speed of a wave is:
Speed (v) = Wavelength (λ) / Time (T)
Substituting the given values:
Speed (v) = 1.50m / 5.00s
Calculating the speed:
Speed (v) = 0.30 m/s
Therefore, the speed of the waves is 0.30 m/s.