Five pulses are generated every 0.094 s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.14 cm?
can you break it down please.
F = 5 / 0.094 = 53.2 Pulses/s =
frequency of pulses.
T = 1/F = 1/53.2
L = VT,
V = L/T = LF,
V = 1.14cm * 53.2pulses/s = 60.6cm/s.
L = wavelength in cm.
F = frequency in pulses / s.
T = Period of frequency.
.
Sure! Let's break down the problem step by step.
Step 1: Identify the given information
- Five pulses are generated every 0.094 s
- The wavelength of the surface wave is 1.14 cm
Step 2: Recall the wave equation
The speed of propagation of a wave (v) is given by the equation:
v = λ / T
where v is the speed of propagation, λ is the wavelength, and T is the period of the wave.
Step 3: Calculate the period (T)
The period is the time it takes for one complete cycle or pulse. In this case, we are given that five pulses are generated every 0.094 s, so the period can be calculated by dividing the total time by the number of pulses:
T = 0.094 s / 5
Step 4: Calculate the speed of propagation (v)
Using the wave equation, we can substitute the calculated period (T) and the given wavelength (λ) into the equation to find the speed of propagation (v):
v = λ / T
Step 5: Insert the values and calculate
Substitute the values of wavelength (1.14 cm) and period (0.094 s / 5) into the equation:
v = 1.14 cm / (0.094 s / 5)
Step 6: Simplify the equation
To simplify the equation, we can multiply the numerator and denominator by 5 to get rid of the fraction:
v = (1.14 cm * 5) / 0.094 s
Step 7: Calculate the speed of propagation (v)
Using a calculator, solve the equation to find the speed of propagation (v):
v ≈ 60.64 cm/s (rounded to two decimal places)
Therefore, the speed of propagation of the wave is approximately 60.64 cm/s.
To find the speed of propagation of the wave, we can use the formula:
Speed = Frequency * Wavelength
Given that the pulses are generated every 0.094 s and the wavelength of the wave is 1.14 cm, we need to determine the frequency first.
The frequency of a wave is the number of oscillations or pulses that occur in 1 second (or any fixed time period).
Frequency = Number of oscillations / Time
In this case, the number of oscillations is given as five pulses and the time is 0.094 s.
So, the frequency of the wave is:
Frequency = 5 / 0.094
To calculate the speed, we simply multiply the frequency by the wavelength:
Speed = Frequency * Wavelength
Now, we can substitute the values:
Speed = (5 / 0.094) * 1.14 cm/s
Calculate the value inside the parentheses:
Speed ≈ 53.19 * 1.14 cm/s
Finally, solve the multiplication:
Speed ≈ 60.7 cm/s
The speed of propagation of the wave in the tank of water is approximately 60.7 cm/s.