Standing waves are produced in a string that is 4.0 m long. If the waves are travelling at 125 cm/s and the distance between the first and the fifth nodes is 80.0 cm, find the frequency of the waves.
Use f=nv/(2L)
f = 5*1.25m/s/(2*4.0 m)
f=.781 Hz
To find the frequency of the waves, we need to know the number of nodes between the first and the fifth nodes.
The distance between the first and fifth nodes is equal to half of the wavelength of the wave.
Given that the distance between the first and fifth nodes is 80.0 cm, we can calculate the wavelength:
Wavelength = 2 * Distance between first and fifth nodes
Wavelength = 2 * 80.0 cm = 160.0 cm = 1.60 m
Now, we can use the equation for wave speed:
Wave speed = Frequency * Wavelength
Given that the wave speed is 125 cm/s and the wavelength is 1.60 m, we can rearrange the equation to find the frequency:
Frequency = Wave speed / Wavelength
Frequency = 125 cm/s / 1.60 m = 12500 cm/m / 1.60 m = 7812.5 Hz
Therefore, the frequency of the waves is 7812.5 Hz.
To find the frequency of the waves, we can use the formula:
frequency = wave speed / wavelength
First, let's calculate the wavelength.
The distance between two consecutive nodes in a standing wave is one-half of a wavelength. In this case, the distance between the first and the fifth nodes is given as 80.0 cm.
So, one-half of the wavelength (λ/2) is equal to 80.0 cm.
To find the full wavelength (λ), we can multiply this by 2:
λ = 2 * 80.0 cm = 160.0 cm
Now, let's convert the wavelength to meters since the length of the string is given in meters:
λ = 160.0 cm = 1.60 m (since 1 m = 100 cm)
Next, we can substitute the given values into the formula to find the frequency:
wave speed = 125 cm/s
wavelength = 1.60 m
frequency = wave speed / wavelength
frequency = 125 cm/s / 1.60 m
To divide by meters, we need to convert cm/s to m/s:
1 m = 100 cm
125 cm/s = 125 cm/s * (1 m/100 cm) = 1.25 m/s
Now we can substitute the values:
frequency = 1.25 m/s / 1.60 m
Finally, we can calculate the frequency:
frequency = 0.78125 Hz (rounded to five decimal places)