Question

A 2-g string that is 0.79 m long is fixed at both ends and is under tension. This string produces a 500-Hz tone when it vibrates in the third harmonic. The speed of sound in air is 344 m/s. The tension in the string, in is closest to __________

Answer 1

`T = 175.6 N`

Step-by-step explanation:

As we know that string is vibrating in third harmonic

So we will have

`L = 3(\lambda)/(2)`

so we have

`0.79 = (3)/(2)\lambda`

so we have

`\lambda = (2)/(3)(0.79)`

`\lambda = 0.527`

we know that frequency of the wave is given as

f = 500 Hz

now we know that

speed of the wave is

`v = frequency * wavelength`

`v = (500)(0.527)`

`v = 263.3 m/s`

now we have

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

so we have

`263.3 \sqrt{(T)/((0.002/0.79))}`

`T = 175.6 N`