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.