Question

A 100-gram wire that is 1.0 m long is under tension. When a transverse wave of frequency 800 Hz travels down the wire, its wavelength is 0.10 m and its amplitude is 6.5 mm. What is the tension in the wire?

Answer 1

T = 640N

Step-by-step explanation:

In order to calculate the tension on the wire you use the following formula:

`v=\sqrt{(T)/(m/L)}\\\\T=(v^2m)/(L)` (1)

T: tension on the wire

v: speed of the transverse wave

L: length of the wire = 1.0 m

m: mass of the wire = 100 g = 0.1kg

Then, you need to calculate the speed of the wave by using the information about the wavelength and the frequency of the wave. You use the following formula:

`v=\lambda f` (2)

λ: wavelength = 0.10 m

f: frequency = 800Hz

You replace the values of the parameters in the equation (2):

`v=(0.10m)(800Hz)=80(m)/(s)`

Next, with the information about the speed of the wave you can calculate the tension on the wire by using the equation (1):

`T=((80m/s)^2(0.1kg))/(1.0m)=640N`

The tension on the wire is 640 N