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katen-ka-za [31]
4 years ago
7

a wave travels in a string at 58 m/s. a second string of 10% greater linear density has the same tension applied as in the first

string. what will be the resulting wave speed in the second string
Physics
1 answer:
ozzi4 years ago
5 0

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

v_{1}=\sqrt{\dfrac{T}{\mu_{1}}}...(I)

For second string

v_{2}=\sqrt{\dfrac{T}{\mu_{2}}}...(II)

Divided equation (II) by equation (I)

\dfrac{v_{2}}{v_{1}}=\sqrt{\dfrac{\dfrac{T}{\mu_{2}}}{\dfrac{T}{\mu_{1}}}}

Here, Tension is same in both string

So,

\dfrac{v_{2}}{v_{1}}=\sqrt{\dfrac{\mu_{1}}{\mu_{2}}}

The linear density of the second string

\mu_{2}=\mu_{1}+\dfrac{10}{100}\mu_{1}

\mu_{2}=\dfrac{110}{100}\mu_{1}

\mu_{2}=1.1\mu_{1}

Now, Put the value of linear density of second string

\dfrac{v_{2}}{v_{1}}=\sqrt{\dfrac{\mu_{1}}{1.1\mu_{1}}}

v_{2}=v_{1}\times\sqrt{\dfrac{1}{1.1}}

v_{2}=58\times\sqrt{\dfrac{1}{1.1}}

v_{2}=55.3\ m/s

Hence, The speed of wave in the second string is 55.3 m/s.

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