Question

A wire is stretched between two rigid supports vibrate in its fundamental mode with a frequency of 50 Hz. The mass of the wire is 30 g and its linear density is 4 × 10–2 kg m s–1. The speed of the transverse wave at the string is

• A. 25 m s–1
• B. 50 m s–1
• C. 75 m s–1
• D. 100 m s–1

Answer 1

Answer: (C)

75 m s–1

Answer 2

Here, Mass of the wire,

$M = 30g = 30 \times 10^{- 3}kg$Mass per unit length of the wire, $\mu = 4 \times 10^{- 2}kgm^{- 1}$

$\therefore$Length of the wire, L

$= \frac{M}{\mu} = \frac{30 \times 10^{- 3}kg}{4 \times 10^{- 2}kgm^{- 1}} = 0.75m$

For the fundamental mode.

$\lambda = 2L = 2 \times 0.75m = 1.5m$

Speed of the transverse wave,

$v = \upsilon\lambda = (50s^{- 1})(1.5m) = 75ms^{- 1}$