Standing Wave: Calculating Tension Required
How do we calculate the tension required to produce a standing wave on a string?
What is the tension required to produce 1 wavelength of a standing wave on a 0.63 m length of string, if it is driven with a frequency of 54 Hz and has a linear density of 0.035 kg/m?
Calculating Tension for Standing Wave on a String
The tension required to produce 1 wavelength of a standing wave on a 0.63 m length of string is approximately 10.15 N.
To calculate the tension required to produce 1 wavelength of a standing wave on a string, we can use the formula:
Tension = (Linear density) * (Wave speed)²
The wave speed can be determined using the formula:
Wave speed = Frequency * Wavelength
Given that the length of the string is 0.63 m and the frequency is 54 Hz, we can calculate the wavelength as:
Wavelength = Length / Number of nodes = 0.63 m / 2 = 0.315 m
Next, we can calculate the wave speed as:
Wave speed = Frequency * Wavelength = 54 Hz * 0.315 m = 16.83 m/s
Now, we can calculate the tension as:
Tension = (0.035 kg/m) * (16.83 m/s)² ≈ 10.15 N
Therefore, the tension required to produce 1 wavelength of a standing wave on the 0.63 m length of string is approximately 10.15 N.