Question

One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates at $120Hz$. The other end passes over a pulley and supports a $1.50kg$ mass. The linear mass density of the rope is $0.0550kg/m$. How wavelength and speed will change if the mass were increased to $3.00kg$ ?

• A. both decrease by $\sqrt{5}$ times.
• B. both increase by $\sqrt{2}$ times.
• C. both increase by $\sqrt{5}$ times.
• D. both decrease by $\sqrt{2}$ times.

Answer 1

The correct option is B both increase by $\sqrt{2}$ times.

Since the mass becomes twice, the tension in the wire becomes twice.

Hence the speed becomes $\sqrt{2}$ times since it varies with tension as $\sqrt{T}$.

$v=\lambda \nu$

Thus the wavelength also becomes $\sqrt{2}$ times the initial value.