Question

Two strings of equal length are stretched out with equal tension. The second string is four times as massive as the first string. If a wave travels down the first string with velocity v, how fast does a wave travel down the second string?

• A. $\frac{1}{4}v$
• B. $\frac{1}{2}v$
• C. $v$
• D. $2v$
• E. $4v$

Answer 1

The correct option is B $\frac{1}{2}v$

The speed of a transverse wave $v$ in a string of length $l$ , having a tension $T$ is given by ,

$v=\sqrt{T/m}$ ,

where $m=M/l$ mass/unit length of string ,

for first string $v=\sqrt{T/m_1}$ ,

for second string $v^{\prime }=\sqrt{T/m_2}$ ,

now $m_2=M_2/l$ and $m_1=M_1/l$ ,

given $M_2=4M_1$ or $m_2=4m_1$ ,

dividing $v^{\prime }$ by $v$ ,

we get $v^{\prime }/v=\sqrt{m_1/m_2}$

or $v^{\prime }/v=\sqrt{m_1/4m_1}=\sqrt{1/4}$

or $v^{\prime }/v=1/2$

or $v^{\prime }=v/2$