A wave travels in a string at 64 m/s.A second string of 25% greater linear density has the same tension applied as in the first string.What will be the resulting wave speed in the second string?

A) also 64 m/s
B) 74 m/s
C) 128 m/s
D) 57 m/s
E) 72 m/s

Question

A wave travels in a string at 64 m/s.A second string of 25% greater linear density has the same tension applied as in the first string.What will be the resulting wave speed in the second string?
​
A) also 64 m/s
B) 74 m/s
C) 128 m/s
D) 57 m/s
E) ​72 m/s

Quizplus · Accepted Answer

The wave speed in a string is given by $ v = \sqrt{\frac{T}{\mu}} $, where $ T $ is the tension and $ \mu $ is the linear density. If the second string has 25% greater linear density, its linear density is $ 1.25\mu $. The wave speed in the second string is $ v_2 = \sqrt{\frac{T}{1.25\mu}} = \frac{v_1}{\sqrt{1.25}} $. Substituting $ v_1 = 64 \, \text{m/s} $, we get $ v_2 = \frac{64}{\sqrt{1.25}} \approx 57 \, \text{m/s} $.

A Wave Travels in a String at 64 M/s