Question

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

Answer 1

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.