Question

question 28 (1 point)
a string of mass m and length l is under tension t. the speed of a wave in the string
is v. what will be the speed of a wave in the string if the tension is increased to 2t?
0.5t
0.71t
1.4t
2t

Explanation:

Step1: Recall wave speed formula on string

The speed \( v \) of a wave on a string with tension \( T \), mass \( m \), and length \( L \) is given by \( v = \sqrt{\frac{T}{\mu}} \), where \( \mu=\frac{m}{L} \) (linear mass density). So initially, \( v = \sqrt{\frac{T}{\mu}} \).

Step2: Find new speed with tension \( 2T \)

Let the new speed be \( v' \). Then \( v' = \sqrt{\frac{2T}{\mu}} \).

Step3: Relate \( v' \) and \( v \)

Divide \( v' \) by \( v \): \( \frac{v'}{v}=\frac{\sqrt{\frac{2T}{\mu}}}{\sqrt{\frac{T}{\mu}}}=\sqrt{2}\approx1.414 \approx 1.4 \). So \( v'\approx1.4v \) (note: the options have \( T \) but it should be related to \( v \); assuming a typo and the options are in terms of the original speed factor, the factor is \( \sqrt{2}\approx1.4 \)).

Answer:

1.4T (assuming the options have a typo and the 'T' is for the speed factor relative to original speed \( v \), the correct factor is \( \sqrt{2}\approx1.4 \))