Respuesta :
Answer:
The speed of wave in the second string is 55.3 m/s.
Explanation:
Given that,
Speed of wave in first string= 58 m/s
We need to calculate the wave speed
Using formula of speed for first string
[tex]v_{1}=\sqrt{\dfrac{T}{\mu_{1}}}[/tex]...(I)
For second string
[tex]v_{2}=\sqrt{\dfrac{T}{\mu_{2}}}[/tex]...(II)
Divided equation (II) by equation (I)
[tex]\dfrac{v_{2}}{v_{1}}=\sqrt{\dfrac{\dfrac{T}{\mu_{2}}}{\dfrac{T}{\mu_{1}}}}[/tex]
Here, Tension is same in both string
So,
[tex]\dfrac{v_{2}}{v_{1}}=\sqrt{\dfrac{\mu_{1}}{\mu_{2}}}[/tex]
The linear density of the second string
[tex]\mu_{2}=\mu_{1}+\dfrac{10}{100}\mu_{1}[/tex]
[tex]\mu_{2}=\dfrac{110}{100}\mu_{1}[/tex]
[tex]\mu_{2}=1.1\mu_{1}[/tex]
Now, Put the value of linear density of second string
[tex]\dfrac{v_{2}}{v_{1}}=\sqrt{\dfrac{\mu_{1}}{1.1\mu_{1}}}[/tex]
[tex]v_{2}=v_{1}\times\sqrt{\dfrac{1}{1.1}}[/tex]
[tex]v_{2}=58\times\sqrt{\dfrac{1}{1.1}}[/tex]
[tex]v_{2}=55.3\ m/s[/tex]
Hence, The speed of wave in the second string is 55.3 m/s.
